MATH 542 NUMERICAL SOLUTIONS OF DIFFERENTIAL EQUATIONS

FINITE ELEMENT METHOD

In this chapter the Finite Element Method and its various forms will be developed for Boundary Values Problems.  The basic idea is to use the differential equation and the boundary values to find the "best" approximate solution taken from a finite dimensional function subspace.  This finite dimensional function subspace will usually be either piecewise linear or piecewise cubic Hermite polynomials.  Things to remember from Math 541 are Cubic Hermite Interpolation, and Linear System Solving Methods   (LU Decomposition, Tridiagonal, Gauss-Seidel and SOR).

1-DIMENSIONAL CASE

    Subdomain
        Piecewise Linear   MATLAB CODE

    Collocation
        Piecewise Linear   MATLAB CODE
        Piecewise Cubic Hermite

    Galerkin
        Piecewise Linear  MATLAB CODE
        Piecewise Cubic Hermite 

2-DIMENSIONAL CASE

    Galerkin
        Linear Triangular  MATLAB CODE

Revised 12/06/04
By Don Short, dshort@sciences.sdsu.edu