MATH 6374: Numerical Partial Differential Equations, Spring 2012


Time of classes:  MW 1:00 - 2:30 PM
Classroom:  F162

My office:  PGH 682
Office hours:  MW 11:00 AM - 12:30 PM or by appointment
 

    The prerequisites for the class are undergraduate courses on partial differential equations and numerical analysis.

    Upon completion of the course, students will be able to apply Finite Difference, Finite Volume, and Finite Element methods for numerical solution of elliptic and parabolic partial differential equations. The course consists of three major parts. In the beginning of the course, we will discuss the differential and variational formulations of the most typical boundary value problems for the diffusion and convection-diffusion equations. In the second part of the course, a systematic description of finite difference, finite volume and nodal finite element methods will be given. We shall also consider the simplest variants of the mixed finite element method, which is currently very popular in many applications. Finally, we will study explicit and implicit finite difference methods for the time dependent diffusion and convection-diffusion equations.

    The course grades will be based on solutions of two Homework sets and results of one quiz, as well as their individual review held in person between the instructor and every student in the end of the semester.

    The recommended text book for the course is:
        Stig Larsson, Vidar Thomée, Partial Differential Equations with Numerical Methods, Springer-Verlag, 2003