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H1 Stability and Convergence of the FE, FV and FD Methods for an Elliptic Equation

Published online by Cambridge University Press:  28 May 2015

Yinnian He*
Affiliation:
Center for Computational Geosciences, School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an 710049, China
Xinlong Feng*
Affiliation:
College of Mathematics and Systems Science, Xinjiang University, Urumqi 830046, China
*
Corresponding author. Email: heyn@mail.xjtu.edu.cn
Corresponding author. Email: fxlmath@gmail.com
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Abstract

We obtain the coefficient matrices of the finite element (FE), finite volume (FV) and finite difference (FD) methods based on P1-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 H1-stability and convergence. Some numerical tests are made, to compare the numerical results from the three methods and to review our theoretical results.

Type
Research Article
Copyright
Copyright © Global-Science Press 2013

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