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An Efficient Numerical Solution Method for Elliptic Problems in Divergence Form

Published online by Cambridge University Press:  03 June 2015

Ali Abbas
Ali Abbas*
Affiliation:
Department of Mathematics, Lebanese International University, Bekaa-Rayak, Lebanon
*
*Corresponding author. Email: ali.abbas@liu.edu.lb
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Abstract

In this paper the problem − div(a(x,y)∇u) = f with Dirichlet boundary conditions on a square is solved iteratively with high accuracy for u and ∇u using a new scheme called “hermitian box-scheme”. The design of the scheme is based on a “hermitian box”, combining the approximation of the gradient by the fourth order hermitian derivative, with a conservative discrete formulation on boxes of length 2h. The iterative technique is based on the repeated solution by a fast direct method of a discrete Poisson equation on a uniform rectangular mesh. The problem is suitably scaled before iteration. The numerical results obtained show the efficiency of the numerical scheme. This work is the extension to strongly elliptic problems of the hermitian box-scheme presented by Abbas and Croisille (J. Sci. Comput., 49 (2011), pp. 239-267).

Keywords

65N3565N08Hermitian schemebox-schemeKronecker productfast solveriterative methodPoisson problem
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 6 , Issue 3 , June 2014 , pp. 327 - 344
Copyright
Copyright © Global-Science Press 2014

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