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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  and
Xinlong Feng
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: [email protected]
Corresponding author. Email: [email protected]
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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.

Keywords

35Q3065N30Finite element methodfinite difference methodfinite volume methodPoisson equationstability and convergence
Type
Research Article
Information
East Asian Journal on Applied Mathematics , Volume 3 , Issue 2 , May 2013 , pp. 154 - 170
Copyright
Copyright © Global-Science Press 2013

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