Books and Thesis

• Yu. Vassilevski, M. Olshanskii, S. Simakov, A. Kolobov, A. Danilov, Personalized Computational Hemodynamics: Models, Methods, and Applications for Vascular Surgery and Antitumor Therapy, Elsevier, March 2020 / ISBN 9780128156537;
   
• Geometrically Unfitted Finite Element Methods and Applications , Bordas, S.P., Burman, E., Larson, M.G., Olshanskii, M.A. (Eds.) Lecture Notes in Computational Science and Engineering series, V. 121  Springer, 2018;
   
• Maxim A. Olshanskii and Eugene E. Tyrtyshnikov, Iterative Methods for Linear Systems: Theory and Applications , SIAM, July 2014 / approx. xiv + 244 / ISBN 978-1-611973-45-7;
   
• Yu.V. Vassilevski, M.A. Olshanskii, Short course on multigrid and domain decomposition methods, Moscow State University: MAKS-Press, Moscow, 2007, Full text in russian is available here;
   
• M.A. Olshanskii, Lectures and exercises in multigrid methods, Fizmatlit: Moscow 2005;
   
• M.A. Olshanskii, Robust multigrid and preconditioned iterative methods, Habilitation Thesis, (2006) pdf-file ;
   

Journal papers

• 2024

  • M. Olshanskii, L. Rebholz, Approximating a branch of solutions to the Navier--Stokes equations by reduced-order modeling, pdf-file;
     
  • A. Mamonov, M. Olshanskii, Analysis of a tensor POD-ROM for parameter dependent parabolic problems, (to appear in SIAM J. Num. Anal.) pdf-file;
     
  • Y  He, M.  Olshanskii, A preconditioner for the grad-div stabilized equal-order finite elements discretizations of the Oseen problem, pdf-file;
     
  • M. Olshanskii, H.  von Wahl , A conservative Eulerian finite element method for transport and diffusion in moving domains, pdf-file;
     
  • M. Olshanskii, A. Reusken, P. Schwering, An Eulerian finite element method for tangential Navier-Stokes equations on evolving surfaces, Mathematics of Computation V.  93 (2024), 2031--2065; pdf-file;
     
  • M. Neilan, M. Olshanskii, An Eulerian finite element method for the linearized Navier-Stokes problem in an evolving domain, IMA Journal of Numerical Analysis (2024), Article drad105; doi: 10.1093/imanum/drad105 pdf-file;
     
  • M. Olshanskii, L. Rebholz, Local conservation laws of continuous Galerkin method for the incompressible Navier-Stokes equations in EMAC form, Computer Methods in Applied Mechanics and Engineering V.  418 (2024), Article 116583; doi: 10.1016/j.cma.2023.116583, pdf-file;
     
  • T. Heister, M. Olshanskii, V. Yushutin, An adaptive stabilized trace finite element method for surface PDEs, Computers \& Mathematics with Applications V.  171 (2024), 164--174; pdf-file;
     
  • A. Mamonov, M. Olshanskii, Tensorial parametric model order reduction of nonlinear dynamical systems, SIAM Journal on Scientific Computing, V. 46 (3) (2024), A1850-A1878; pdf-file;
     

• 2023

  • Y. Wang, Y. Palzhanov, D Dang, A. Quaini, M. Olshanskii, S. Majd, On fusogenicity of positively charged phased-separated lipid vesicles: experiments and computational simulations, Biomolecules V.  13 (2023), Article 1473; doi: 10.3390/biom13101473; 
     
  • M. Olshanskii, Y. Palzhanov, A. Quaini, A scalar auxiliary variable unfitted FEM for the surface Cahn-Hilliard equation, Journal of Scientific Computing V.  97 (2023), Article 57; doi: 10.1007/s10915-023-02370-8;  pdf-file;
     
  • M. Olshanskii, On equilibrium states of fluid membranes, featured paper in Physics of Fluids, V.  35 (2023), Article 062111; pdf-file;
     
  • H.  Liu, M.  Neilan, M. Olshanskii, A CutFEM divergence--free discretization for the Stokes problem, ESAIM: Mathematical Modelling and Numerical Analysis, V.  57 (2023), 143--165;  doi: 10.1051/m2an/2022072;  pdf-file;
     

• 2022

  • M. Olshanskii, A. Reusken, A. Zhilyakov, Tangential Navier-Stokes equations on evolving surfaces: Analysis and simulations, Mathematical Models and Methods in Applied Sciences V.  14 (2022), 2817-2852; doi: 10.1142/S0218202522500658;  pdf-file;
     
  • A. Mamonov, M. Olshanskii, Interpolatory tensorial reduced order models for parametric dynamical systems, Computer Methods in Applied Mechanics and Engineering V.  397 (2022), Article 115122; doi: 10.1016/j.cma.2022.115122, pdf-file;
     
  • A.  Lozovskiy, M.A.  Olshanskii, Y.V.  Vassilevski, A finite element scheme for the numerical solution of the Navier-Stokes / Biot coupled problem, pdf-file;
     
  • Y.  Wang, Y.  Palzhanov, A. Quaini, M. Olshanskii, S. Majd, Lipid domain coarsening and fluidity in multicomponent lipid vesicles: A continuum based model and its experimental validation,   BBA - Biomembranes, V.  29 (2022), Article e2415;   doi: 10.1016/j.bbamem.2022.183898,   pdf-file;
     
  • M. Olshanskii, A.  Zhiliakov, Recycling augmented Lagrangian preconditioner in an incompressible fluid solver, Numerical Linear Algebra with Applications , V.  1864 (2022), Article 183898; doi: 10.1002/nla.2415, pdf-file;
     
  • M. Olshanskii, Y.  Palzhanov, Q.  Sun, A comparison of Cahn-Hilliard and Navier-Stokes-Cahn-Hilliard models on manifolds, Vietnam Journal of Mathematics,   doi: 10.1007/s10013-022-00564-5,   pdf-file;
     
  • M. Olshanskii, A.  Quaini, Q.  Sun, A finite element method for two-phase flow with material viscous interface, Computational Methods in Applied Mathematics , V.  22 (2022), p.443-464 pdf-file;
     

• 2021

  • Y.  Palzhanov, A.  Zhiliakov, A.  Quaini, M.  Olshanskii, A decoupled, stable, and linear FEM for a phase-field model of variable density two-phase incompressible surface flow, Computer Methods in Applied Mechanics and Engineering, V.  387 (2021), Article 114167;   doi: 10.1016/j.cma.2021.114167, pdf-file;
     
  • A.  Lozovskiy, M.A.  Olshanskii, Y.V.  Vassilevski, A monolithic fluid-porous structure interaction finite element method, pdf-file;
     
  • M. Olshanskii, A.  Quaini, Q.  Sun, An unfitted finite element method for two-phase Stokes problems with slip between phases, Journal of Scientific Computing, V.  89 (2021), Article 41; SharedIt or pdf-file;
     
  • A.  Zhiliakov, Y.  Wang, A. Quaini, M. Olshanskii, S. Majd, Experimental validation of a phase-field model to predict coarsening dynamics of lipid domains in multicomponent membranes, BBA - Biomembranes, V.  1863 (2021), Article 183446;   doi: 10.1016/j.bbamem.2020.183446   pdf-file;
     
  • M. Olshanskii, X.  Xu, V.  Yushutin, A finite element method for Allen--Cahn equation on deforming surface, Computers & Mathematics with Applications, V.  90 (2021), p. 148-158;   pdf-file;
     
  • M. Olshanskii, A.  Reusken, A.  Zhiliakov, Inf-sup stability of the trace P2-P1 Taylor-Hood elements for surface PDEs, Mathematics of Computation V.  90 (2021), p. 1527-1555; doi: 10.1090/mcom/3551,  pdf-file;
     
  • T. Junkuhn, M. Olshanskii, A.  Reusken, A.  Zhiliakov, Error analysis of higher order trace finite element methods for the surface Stokes equations, Journal of Numerical Mathematics, V.  29 (2021), p. 245-267;   doi: 10.1515/jnma-2020-0017 , pdf-file;
     

• 2020

  • M. Olshanskii, Speed-direction description of turbulent flows, Physics of Fluids, V.  32 (2020), Article 115128;   doi: 10.1063/5.0031218, pdf-file;
     
  • Y. Vassilevski, A. Danilov, A. Lozovskiy, M. Olshanskii, V. Salamatova, S Chang, Y. Han, C. H. Lin, A stable method for 4D CT-based CFD simulation in the right ventricle of a TGA patient, Rus.J.Num.Anal.Math.Model., V.  35 (2020), p. 315-324; pdf-file;
     
  • M. Olshanskii, L.  Rebholz, Longer time accuracy for incompressible Navier-Stokes simulations with the EMAC formulation, Computer Methods in Applied Mechanics and Engineering, V.  372 (2020), Article 113369;   doi: 10.1016/j.cma.2020.113369, pdf-file;
     
  • E.  Caceres, J. Guzman, M. Olshanskii, New stability estimates for an unfitted finite element method for two-phase Stokes problem, SIAM J. Numer. Anal., V.  58 (2020), p. 2165-2192;   doi: 10.1137/19M1266897, pdf-file;
     
  • V.  Yushutin, A. Quaini, M. Olshanskii, Numerical modelling of phase separation on dynamic surfaces, Journal of Computational Physics; V.  407 (2020), Article 109126;   doi: 10.1016/j.jcp.2019.109126, pdf-file;
     
  • A.  Chernyshenko, M. Olshanskii, An unfitted finite element method for the Darcy problem in a fracture network, Journal of Computational and Applied Mathematics; V.  336 (2020), Article 112424;  doi: 10.1016/j.cam.2019.112424,  pdf-file;
     

• 2019

  • A. Zhiliakov, D. Svyatsky, M. Olshanskii, E. Kikinzon, M. Shashkov, A higher order approximate static condensation method for multi-material diffusion problems, Journal of Computational Physics; V.  395 (2019), 333-350;  10.1016/j.jcp.2019.06.044;  pdf-file,
     
  • V.  Yushutin, A. Quaini, S. Majd, M. Olshanskii, A computational study of lateral phase separation in biological membranes, International Journal for Numerical Methods in Biomedical Engineering, V. 35 (2019), e3182;  doi: 10.1002/cnm.3181;  pdf-file;
     
  • M. Olshanskii, V.  Yushutin, A penalty finite element method for a fluid system posed on embedded surface, Journal of Mathematical Fluid Mechanics, V.  21 (2019), 14-31;  doi: 10.1007/s00021-019-0420-y;  pdf-file;
     
  • A. Lozovskiy, M. Olshanskii, Yu. Vassilevski, Analysis and assessment of a monolithic FSI finite element method, Computers & Fluids, V.  179 (2019), 277-288   doi: 0.1016/j.compfluid.2018.11.004;  pdf-file;
     
  • C. Lehrenfeld, M. Olshanskii, An Eulerian Finite Element Method for PDEs in time-dependent domains, ESAIM: Mathematical Modelling and Numerical Analysis, V.  53 (2019), 585-614;  doi: 10.1051/m2an/2018068;  pdf-file;
     
  • S. Charnyi, T. Heister, M.A. Olshanskii, L.G. Rebholz, Efficient discretizations for the EMAC formulation of the incompressible Navier-Stokes equations, Applied Numerical Mathematics, V.  141 (2019), 220-233;  doi: 10.1016/j.apnum.2018.11.013;  pdf-file;
     
  • I.N. Konshin, M.A. Olshanskii, Yu.V. Vassilevski, An algebraic solver for the Oseen problem with application to hemodynamics, Contributions to Partial Differential Equations and Applications, V. 47 (2019), 339-357, pdf-file;
     

• 2018

  • M. Olshanskii, A. Quaini, A. Reusken, V. Yushutin, A finite element method for the surface Stokes problem, SIAM J.Sci.Comp. V. 40 (2018), A2492-A2518   pdf-file;
     
  • C. Lehrenfeld, M. Olshanskii, X. Xu, A stabilized trace finite element method for partial differential equations on evolving surfaces, SIAM J.Numer.Anal. V. 56 (2018), 1643-1672, pdf-file;
     
  • Th.  Jankuhn, M.A. Olshanskii, A. Reusken, Incompressible fluid problems on embedded surfaces: Modeling and variational formulations, Interfaces and Free Boundaries V. 20 (2018), 353-377, pdf-file;
     
  • S. Gross, T. Jankuhn, M. Olshanskii, A. Reusken, A Trace Finite Element Method for Vector-Laplacians on Surfaces, SIAM J.Numer.Anal. V. 56 (2018), 2406-2429, pdf-file;
     
  • M. Olshanskii, L. Rebholz, A. Salgado, On well-posedness of a velocity-vorticity formulation of the Navier-Stokes equations with no-slip boundary conditions, Discrete and Continuous Dynamical Systems, Series A, V. 38 (2018), 3459-3477, pdf-file;
     
  • J. Guzman, M.A. Olshanskii, Inf-sup stability of geometrically unfitted Stokes finite elements, Mathematics of Computation V. 87 (2018), 2091-2112, pdf-file;
     
  • review paper: M.A. Olshanskii, A. Reusken, Trace Finite Element Methods for PDEs on Surfaces, in Lecture Notes in Computational Science and Engineering series, V. 121 (2018), 211-258, pdf-file;
     
  • K.D. Nikitin, M.A. Olshanskii, K.M. Terekhov, Yu.V. Vassilevski, A splitting method for free surface flows over partially submerged obstacles, Rus.J.Num.Anal.Math.Model. V. 33 (2018), 95-110, pdf-file;
     
  • A. Lozovskiy, M. Olshanskii, Yu. Vassilevski, A quasi-Lagrangian finite element method for the Navier-Stokes equations in a time-dependent domain, Computer Methods in Applied Mechanics and Engineering, V. 333 (2018), 55-73, pdf-file;
     
  • A.Y. Chernyshenko, M.A. Olshanskii, Yu.V. Vassilevski, A hybrid finite volume-finite element method for bulk-surface coupled problems, Journal of Computational Physics, V. 352 (2018), 516-533, pdf-file;
     

• 2017

  • A. Danilov, A. Lozovskiy, M. Olshanskii, Yu. Vassilevski, A finite element method for the Navier-Strokes equations in moving domain with application to hemodynamics of the left ventricle, Rus.J.Num.Anal.Math.Model. V. 32 (2017), 225-236, pdf-file;
     
  • M.A. Olshanskii, X. Xu, A trace finite element method for PDEs on evolving surfaces, SIAM J.Sci.Comp. V. 39 (2017), A1301-A1319 pdf-file;
     
  • S. Charnyi, T. Heister, M.A. Olshanskii, L.G. Rebholz, On conservation laws of Navier-Stokes Galerkin discretizations, Journal of Computational Physics, V. 337 (2017), 289-308, pdf-file;
     
  • K.D. Nikitin, M.A. Olshanskii, K.M. Terekhov, Yu.V. Vassilevski, R. Yanbarisov, An adaptive numerical method for free surface flows passing rigidly mounted obstacles, Computers & Fluids, V. 148 (2017), 56-68, pdf-file;
     
  • W. Cheng, M.A. Olshanskii, Finite stopping times for freely oscillating drop of a yield stress fluid, Journal of Non-Newtonian Fluid Mechanics V. 239 (2017), 73-84, pdf-file;
     
  • T. Heister, M.A. Olshanskii, L.G. Rebholz, Unconditional long-time stability of a velocity-vorticity method for the 2D Navier-Stokes equations, Numerische Mathematik, V. 135  (2017), 143-167 pdf-file;
     
  • I.N. Konshin, M.A. Olshanskii, Yu.V. Vassilevski, LU factorizations and ILU preconditioning for stabilized discretizations of incompressible Navier-Stokes equations, Numerical Linear Algebra with Applications, V. 24  Issue 3 (2017) doi: 10.1002/nla.2085 pdf-file;
     

• 2016

  • T.K.. Dobroserdova, M.A. Olshanskii, S.S. Simakov, Multiscale coupling of compliant and rigid walls blood flow models, Int.J.Numer.Meth.Fluids V. 82 (2016), 799-817, pdf-file;
     
  • M.A. Olshanskii, D. Safin, Numerical integration over implicitly defined domains for higher order unfitted finite element methods, Lobachevskii Journal of Mathematics V. 37 (2016), 582-596, pdf-file;
     
  • S. Gross, T. Ludescher, M.A. Olshanskii, A. Reusken, Robust preconditioning for XFEM applied to time-dependent Stokes problems, SIAM J.Sci.Comp. V. 38 (2016), A3492-A3514 pdf-file;
     
  • M.A. Olshanskii, D. Safin, A narrow-band unfitted finite element method for elliptic PDEs posed on surfaces, Mathematics of Computation, V. 85 (2016), 1549-1570, pdf-file;
     

• 2015

  • K.M. Terekhov, K.D. Nikitin, M.A. Olshanskii, Y.V.. Vassilevski, A semi-Largangian method on dynamically adapted octree meshes, Rus.J.Num.Anal.Math.Model. V. 30 (2015), 363-380, pdf-file;
     
  • A. Lozovskiy, M.A. Olshanskii, V. Salamatova, Yu.V. Vassilevski, An unconditionally stable semi-implicit FSI finite element method, Computer Methods in Applied Mechanics and Engineering, V. 297 (2015), 437-454, pdf-file;
     
  • M.A. Olshanskii, T. Heister, L.G. Rebholz, K.J. Galvin, Natural vorticity boundary conditions on solid walls, Computer Methods in Applied Mechanics and Engineering, V. 297 (2015), 18-37, pdf-file;
     
  • I.N. Konshin, M.A. Olshanskii, Yu.V. Vassilevski, ILU preconditioners for non-symmetric saddle point matrices with application to the incompressible Navier-Stokes equations, SIAM J.Sci.Comp., V. 37 (2015), A2171-A2197, pdf-file;
     
  • K.D. Nikitin, M.A. Olshanskii, K.M. Terekhov, Yu.V. Vassilevski, A splitting method for numerical simulation of free surface flows of incompressible fluids with surface tension, Computational Methods in Applied Mathematics , V. 15 (2015), 59-77, pdf-file;
     
  • A. Chernyshenko, M.A. Olshanskii, An adaptive octree finite element method for PDEs posed on surfaces, Computer Methods in Applied Mechanics and Engineering, V. 291 (2015), 146-172, doi: 10.1016/j.cma.2015.03.025, pdf-file;
     
  • S. Gross, M.A. Olshanskii, A. Reusken, A trace finite element method for a class of coupled bulk-interface transport problems, ESAIM: Mathematical Modelling and Numerical Analysis, V. 49 (2015), 1303-1330, pdf-file;

• 2014

  • M.A. Olshanskii, A. Reusken, Error analysis of a space-time finite element method for solving PDEs on evolving surfaces, SIAM J.Numer.Anal., V. 52 (2014), 2092-2120, pdf-file;
     
  • M.A. Olshanskii, A. Reusken, X. Xu, An Eulerian space-time finite element method for diffusion problems on evolving surfaces, SIAM J.Numer.Anal., V. 52 (2014), 1354-1377, pdf-file;
     
  • M.A. Olshanskii, A. Reusken, X. Xu, A stabilized finite element method for advection-diffusion equations on surfaces, IMA Journal of Numerical Analysis, V. 28 (2014), 732-758, pdf-file;

• 2013

  • M.A. Olshanskii, A. Reusken, X. Xu, On surface meshes induced by level set functions, Computing and Visualization in Science, V. 15 (2013), 53-60, pdf-file;
     
  • M.A. Olshanskii, K.M. Terekhov, Y.V. Vassilevski, An octree-based solver for the incompressible Navier-Stokes equations with enhanced stability and low dissipation, Computers & Fluids, V. 84 (2013), 231-246, pdf-file; more can be found in PhD thesis of K. Terkhov here;
     
  • M.A. Olshanskii, X. Xiong, A connection between filter stabilization and eddy viscosity models, Numerical Methods for Partial Differential Equations, V. 29 (2013), 2061-2080, pdf-file;
     
  • T.K. Dobroserdova, M.A. Olshanskii, A finite element solver and energy stable coupling for 3D and 1D fluid models, Computer Methods in Applied Mechanics and Engineering, V. 259 (2013), 166-176, pdf-file;
     
  • A.Y. Chernyshenko, M.A. Olshanskii, Non-degenerate Eulerian finite element method for solving PDEs on surfaces, Rus.J.Num.Anal.Math.Model., V. 28 (2013), 101-124, pdf-file; PhD thesis of A. Chernyshenko are here;

• 2012

  • M. Benzi, M.A. Olshanskii, L. Rebholz, Z. Wang, Assessment of a vorticity based solver for the Navier-Stokes equations, Computer Methods in Applied Mechanics and Engineering, V. 247–248 (2012), 216-225, pdf-file;
     
  • K.D. Nikitin, M.A. Olshanskii, K.M. Terekhov, Yu.V. Vassilevski, A CFD approach to the 3D modelling of large-scale hydrodynamic events and disasters, Rus.J.Num.Anal.Math.Model., V. 27 (2012), 399-412, pdf-file;
     
  • A. Demlow, M.A. Olshanskii, An adaptive surface finite element method based on volume meshes, SIAM J.Numer.Anal., V. 50 (2012), 1624-1647, pdf-file;
     
  • M.A. Olshanskii, A fluid solver based on vorticity -- helical density equations with application to a natural convection in a cubic cavity, Int.J.Numer.Meth.Fluids, V. 69 (2012), 983-994, pdf-file;
     
  • M.A. Olshanskii, Multigrid analysis for the time dependent Stokes problem, Mathematics of Computation, V. 81 (2012), 57-79, pdf-file;

• 2011

  • K.D. Nikitin, M.A. Olshanskii, K.M. Terekhov, Yu.V. Vassilevski A numerical method for the simulation of free surface flows of viscoplastic fluid in 3D, J.Comp.Math., V. 29 (2011), 605-622, pdf-file; To playback numerical examples from the paper click here;
     
  • M.A. Olshanskii, L. Rebholz, Application of barycenter refined meshes in linear elasticity and incompressible fluid dynamics, ETNA, V. 38 (2011), 258-274, pdf-file;
     
  • K.D. Nikitin, M.A. Olshanskii, K.M. Terekhov, Yu.V. Vassilevski, Numerical simulations of free surface flows on adaptive cartesian grids with the level set function method, pdf-file. You can playback numerical examples from the paper here. The virtual album  collects some more animated free surface Navier-Stokes solutions computed with this approach;
     
  • A. Aposporidis, E. Haber, M.A. Olshanskii, A. Veneziani, A mixed formulation of the Bingham fluid flow problem: Analysis and numerical solution, Computer Methods in Applied Mechanics and Engineering, V. 200 (2011), 2434-2446, pdf-file;
     
  • C.C. Manica, M. Neda, M.A. Olshanskii, L.G. Rebholz, N.E. Wilson, On an efficient finite element method for Navier-Stokes-omega with strong mass conservation, Computational Methods in Applied Mathematics, V. 11 (2011), 3-22, pdf-file;
     
  • M. Benzi, M.A. Olshanskii, Field-of-values convergence analysis of Augmented Lagrangian preconditioners for the linearized Navier-Stokes problem, SIAM J.Numer.Anal., V. 49 (2011), 770-788, pdf-file;
     
  • H.K. Lee, M.A. Olshanskii, L.G. Rebholz, On error analysis for the 3D Navier-Stokes equations in Velocity-Vorticity-Helicity form, SIAM J.Numer.Anal., V. 49 (2011), 711-732, pdf-file;
     
  • C.C. Manica, M. Neda, M.A. Olshanskii, L.G. Rebholz, Enabling numerical accuracy of the Navier-Stokes-alpha through deconvolution and enhanced stability, ESAIM: Mathematical Modelling and Numerical Analysis, V. 45 (2011), 277-307, pdf-file;
     
  • M. Benzi, M.A. Olshanskii, Z. Wang, Modified augmented Lagrangian preconditioners for the incompressible Navier-Stokes equations, Int.J.Numer.Meth.Fluids, V. 66 (2011), 486-508, pdf-file;

• 2010

  • M.A. Olshanskii, V. Simoncini, Acquired clustering properties and solution of certain saddle point systems, SIAM J.Matrix Anal.Appl., V. 31 (2010), 2754-2768, pdf-file;
     
  • P. Grinevich, M.A. Olshanskii, An iterative method for solving the regularized Bingham problem, Numerical Methods and Programming, V. 11 (2010), 78-87, full text available on the journal cite;
     
  • M.A. Olshanskii, L.G. Rebholz, Velocity-Vorticity-Helicity formulation and a solver for the Navier-Stokes equations, Journal of Computational Physics, V. 229 (2010), 4291-4303, pdf-file;
     
  • M.A. Olshanskii, L.G. Rebholz, A note on helicity balance of the Galerkin method for the 3D Navier-Stokes equations, Computer Methods in Applied Mechanics and Engineering, V. 199 (2010), 1032-1035, pdf-file;
     
  • M.A. Olshanskii, A. Reusken, A finite element method for surface PDEs: Matrix properties, Numerische Mathematik, V. 114 (2010), 491-520, pdf-file;
     
  • M.A. Olshanskii, A. Sokolov, S. Turek, Error analysis of a projection method for the Navier-Stokes equations with Coriolis force, Journal of Mathematical Fluid Mechanics, V. 12 (2010), 485-502, pdf-file;

• 2009

  • M.A. Olshanskii, G. Lube, T. Heister, J. Loewe, Grad-Div stabilization and subgrid pressure models for the incompressible Navier-Stokes equations, Computer Methods in Applied Mechanics and Engineering, V. 198 (2009), 3975-3988, pdf-file;
     
  • P. Grinevich, M.A. Olshanskii, An iterative method for the Stokes type problem with variable viscosity, SIAM J.Sci.Comp., V. 31 (2009), 3959-3978, pdf-file;
     
  • W. Layton, C.C. Manica, M. Neda, M.A. Olshanskii, L.G. Rebholz, On the accuracy of the rotation form in simulations of the Navier-Stokes equations, Journal of Computational Physics, V. 228 (2009), 3433-3447, pdf-file;
     
  • M.A. Olshanskii, Analysis of semi-staggered finite-difference method with application to Bingham flows, Computer Methods in Applied Mechanics and Engineering, V. 198 (2009), 975-985, pdf-file;
     
  • M.A. Olshanskii, A. Reusken, J. Grande, A Finite Element method for elliptic equations on surfaces, SIAM J.Num.Anal., V. 47 (2009), 3339-3358, pdf-file;

• 2008

  • E. Muravleva, M.A. Olshanskii, Two finite-difference schemes for the Bingham cavity flows, Rus.J.Num.Anal.Math.Model., V. 23 (2008), 615-634, pdf-file; preprint in russian is here;
     
  • M.A. Olshanskii, A. Sokolov, S. Turek, Numerical study of a discrete projection method for rotating incompressible flows, ETNA, V. 32 (2008), 49-62, PDF file and additional resources are downloadable here;
     
  • M.A. Olshanskii, A. Sokolov and S. Turek, A discrete projection method for incompressible viscous flow with Coriolis force, Computer Methods in Applied Mechanics and Engineering, V. 197 (2008), 4512-4520, pdf-file;
     
  • M.A. Olshanskii, M. Benzi, An augmented Lagrangian approach to linearized problems in hydrodynamic stability, SIAM J.Sci.Comp., V. 30 (2008), 1459-1473, pdf-file;

• 2006-2007

  • M.A. Olshanskii, Yu. Vassilevski, Pressure Schur complement preconditioners for the discrete Oseen problem, SIAM J.Sci.Comp., V. 29 (2007), 2686-2704, pdf-file;
     
  • M. Benzi, M.A. Olshanskii, An augumented lagrangian-based approach to the Oseen problem, SIAM J.Sci.Comp., V. 28 (2006), 2095-2113, pdf-file;
     
  • M.A. Olshanskii, J. Peters, A. Reusken, Uniform preconditioners for a parameter dependent saddle point problem with application to generalized Stokes interface equations, Numerische Mathematik, V. 105 (2006), 159-191, pdf-file;
     
  • M.A. Olshanskii, A. Reusken, Analysis of a Stokes interface problem, Numerische Mathematik, V. 103 (2006), 129-149, pdf-file;

• 2004-2005

  • T. Gelhard, G. Lube, M.A. Olshanskii, J.-H. Starcke, Stabilized finite element schemes with LBB-stable elements for incompressible flows, Journal of Computational and Applied Mathematics, V. 177 (2005), 243-267, pdf-file;
     
  • M.A. Olshanskii, Analyis of a multigrid method for convection-diffusion problem with Dirichlet boundary conditions, J.Computational Mathem. and Mathem.Physics., V. 44 (2004), 1462-1491, pdf-file  (in Russian);
     
  • M.A. Olshanskii, A. Reusken, Convergence analyis of a multigrid solver for a finite element method applied to convection-dominated model problem, SIAM J.Num.Anal., V. 42 (2004), 1261-1291, pdf-file;
     
  • M.A. Olshanskii, A. Reusken, Grad-Div stabilization for the Stokes equations, Mathematics of Computation, V. 73 (2004), 1699-1718, pdf-file;

• 2000-2003

  • M.A. Olshanskii, A low order Galerkin finite element method for the Navier-Stokes equations of steady incompressible flow: A stabilization issue and iterative methods, Computer Methods in Applied Mechanics and Engineering, V. 191 (2002), 5515-5536, pdf-file;
     
  • M.A. Olshanskii, A. Reusken, Navier-Stokes equations in rotation form: a robust multigrid solver for the velocity problem, SIAM J.Sci.Comp., V. 23 (2002), 1682-1706, pdf-file;
     
  • G. Lube, M.A. Olshanskii, Stable finite element calculations of incompressible flows using the rotation form of convection, IMA J.Num.Anal., V. 22 (2002), 437-461, pdf-file;
     
  • M.A. Olshanskii, A. Reusken, On the convergence of a multigrid method for linear reaction-diffusion problems, Computing, V. 65 (2000), 193-202, pdf-file;
     
  • E.V. Chizhonkov, M.A. Olshanskii, On the domain geometry dependence of the LBB condition, M2AN (Math.Modelling Numer.Anal.), V. 34 (2000), 935-951, zipped ps-file, pdf-file;
     
  • G. Kobelkov, M.A. Olshanskii, Effective Preconditioning of Uzawa Type Schemes for Generalized Stokes Problem, Numerische Mathematik, V. 86 (2000), 443-470, pdf-file;
     
  • E.V. Chizhonkov, M.A. Olshanskii, On the asymptotic of the constant from infsup condition in elongated domains, Mathematical Notes,(Matematicheskie Zametki), V. 67 (2000), 387-396, Russian version of the paper can be downloaded;
     
  • M.A. Olshanskii, V.M. Staroverov, On Simulation of the Outflow Boundary Conditions in FD Calculations for Incompressible Fluid, Int.J.Numer.Meth.Fluids, V. 33 (2000), 499-534, pdf-file;

• 1993-1999

  • M.A. Olshanskii, Iterative solver for Oseen problem and numerical solution of incompressible Navier-Stokes equations, Num.Linear Algebra Appl., V. 6 (1999), 353-378, pdf-file;
     
  • M.A. Olshanskii, Two-Level Method and Some A Priori Estimates in Unsteady Navier-Stokes Calculations, Journal of Computational and Applied Mathematics, V. 104 (1999), 173-191, pdf-file;
     
  • M.A. Olshanskii, On the Stokes problem with model boundary conditions, Sbornik: Mathematics, V. 188 (1997), 603-620 (English translation from Matematicheskii Sbornik) pdf-file in English, ps-file in Russian;
     
  • M.A. Olshanskii, An exact numerical method for solving the Stokes type factorized problem, Journal of Computational Mathematics and Mathematical Physics, V. 37-2 (1997), 198-209;
     
  • M.A. Olshanskii, The Stokes problem with a parameter, Journal of Computational Mathematics and Mathematical Physics, V. 36-2 (1996), 193-202;
     
  • M.A. Olshanskii, On numerical solution of nonstationary Stokes equations, Russ. J. Numer. Anal. Math. Modelling., V. 10-1 (1995), 81-92;
     
  • M.A. Olshanskii, On one iterative method for numerical solution of the Stokes problem, Vestnik MGU, Ser. 15-2 (1993), 72-77 (in Russian);

Papers in conference proceedings

• A.Y. Chernyshenko, M.A. Olshahskii, Y.V. Vassilevski, A Hybrid Finite Volume—Finite Element Method for Modeling Flows in Fractured Media, Finite Volumes for Complex Applications VIII - Hyperbolic, Elliptic and Parabolic Problems. FVCA 2017, DOI: 10.1007/978-3-319-57394-6_55 link;
   
• T.K. Dobroserdova, Y.V. Vassilevski, S.S. Simakov, M.A. Olshanskii, V.Yu. Salamatova, T.M. Gamilov, V.K. Kramarenko, Y.A. Ivanov, The Model of Global Blood Circulation and Applications, 6th European Conference of the International Federation for Medical and Biological Engineering Proceedings, link;
   
• J. Grande, M.A. Olshanskii, A. Reusken, A space-time FEM for PDEs on evolving surfaces, in proceedings of 11th World Congress on Computational Mechanics, (Eds E. Onate, J. Oliver and A. Huerta), 2014, pdf-file;
   
• A. Danilov, K. Nikitin, M.A. Olshanskii, K. Terekhov, and Yu. Vassilevski, A unified approach for computing tsunami, waves, floods, and landslides, Lecture Notes in Computational Science and Engineering, V. 103, Springer, 2014, p. 643-650 pdf-file;
   
• M.A. Olshanskii, A. Reusken, X. Xu, A volume mesh finite element method for PDEs on surfaces, in Proc. of European Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS 2012 (Eds J. Eberhardsteiner et. al.), 2012, pdf-file;
   
• K.D. Nikitin, M.A. Olshanskii, K.M. Terekhov and Yu.V. Vassilevski, Numerical modelling of viscoplastic free surface flows in complex 3D geometries, in Proc. of European Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS 2012 (Eds J. Eberhardsteiner et. al.), 2012, pdf-file;
   
• K.D. Nikitin, M.A. Olshanskii, K.M. Terekhov, Yu.V. Vassilevski, Preserving distance property of level set function and simulation of free surface flows on adaptive grids, in Numerical geometry, grid generation and high perfomance computing, 2010, 25-32;
   
• M.A. Olshanskii, A. Reusken, On a robust multigrid method for convection-diffusion finite element problems, pdf-file;
   
• M.A. Olshanskii, A Stokes interface problem: stability, error estimate and a solver, in Proc. of European Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS 2004 (Eds. P. Neittaanmaki, etc.), 2004, pdf-file;
   
• M.A. Olshanskii, Preconditioned iterations for the linearized Navier-Stokes system in the rotation form, Proceedings Second MIT Conference on Computational Fluid and Solid Mechanics, K.J. Bathe, editor, Elsevier 2003, 1074-1077, pdf-file;
   
• M.A. Olshanskii, A robust iterative solver in simulation of unsteady incompressible Navier-Stokes flow, Proc. Fourth Europ. Comput. Fluid Dynamic Conf., V. 1, (Eds R. Papailiou, etc.), Willey, Chichester, etc. , 1998, 1296-1301, ps-file;
   
• M.A. Olshanskii, On Preconditioning Techniques for Generalized Stokes Problem, Proc. of the Conf. on Precond. Iter. Solution Meth. in Large Scale Probl. in Scientific Comp., (Eds O. Axelsson, M. Neytcheva, B. Polman) Nijmegen, the Netherlands, 1997, 137-144;
   
• G.M. Kobelkov, M.A. Olshanskii, V.M. Staroverov, To numerical solution of the Stokes problem, Proceedings of the conf. on Appl.Math. and Comp.Science, Moscow, 1996, 27-39;
   

PhD thesis of some of my former students

• Andriy Sokolov, Analysis and Numerical Realization of Discrete Projection Methods for Rotating Incompressible Flows, January 2009 (co-supervised with S. Turek) pdf-file;
   
• Petr Grinevich, Numerical solver for the variable viscosity Stokes type problem and applications, March 2011 pdf-file;
   
• Tatiana Dobroserdova, Numerical modeling of blood dynamics in the presence intravenous implants and pathologies, October 2013 pdf-file;
   
• Wang Cheng, Yield stress fluid: analysis and numerical studies, September 2017 pdf-file;
   
• Rita Stanaitute, ILU and Machine Learning based preconditioning for the discretized incompressible Navier--Stokes equations, April 2020 pdf-file;
   
• Qi Sun, Finite element methods and machine learning for some multi-phase problems, April 2022 pdf-file;
   
• Alexander Zhiliakov, Trace finite element method for material surface flows, April 2022 (Department nomination for the University Outstanding Dissertation Award) link or pdf-file
   
• Yerbol Palzhanov, Numerical Phase-Field Models On Surfaces And Applications, April 2024 (Department nomination for the University Outstanding Dissertation Award) pdf-file;