$H^1$-Stability and Convergence of the FE, FV and FD Methods for an Elliptic Equation

Author(s)

Abstract

We obtain the coefficient matrices of the finite element (FE), finite volume (FV) and finite difference (FD) methods based on $P_1$-conforming elements on a quasi-uniform mesh, in order to approximately solve a boundary value problem involving the elliptic Poisson equation. The three methods are shown to possess the same $H^1$-stability and convergence. Some numerical tests are made, to compare the numerical results from the three methods and to review our theoretical results.

Keywords:

Finite element method finite difference method finite volume method Poisson equation stability and convergence.
About this article

Abstract View

  • 40662

Pdf View

  • 4312

DOI

10.4208/eajam.030513.200513a