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Local Multilevel Method on Adaptively Refined Meshes for Elliptic Problems with Smooth Complex Coefficients

Part of: Numerical linear algebra Partial differential equations, boundary value problems

Published online by Cambridge University Press:  05 August 2015

Shishun Li ,
Xinping Shao  and
Zhiyong Si
Shishun Li*
Affiliation:
School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo 454003, P. R.China
Xinping Shao
Affiliation:
School of Science, Hangzhou Dianzi University, Hangzhou 310018, China
Zhiyong Si
Affiliation:
School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo 454003, P. R.China
*
*Email addresses: lss6@sina.com (S.-S. Li), shaoxinping1983@126.com (X.-P. Shao), sizhiyong@hpu.edu.cn (Z.-Y. Si)
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Abstract

In this paper, a local multilevel algorithm is investigated for solving linear systems arising from adaptive finite element approximations of second order elliptic problems with smooth complex coefficients. It is shown that the abstract theory for local multilevel algorithm can also be applied to elliptic problems whose dominant coefficient is complex valued. Assuming that the coarsest mesh size is sufficiently small, we prove that this algorithm with Gauss-Seidel smoother is convergent and optimal on the adaptively refined meshes generated by the newest vertex bisection algorithm. Numerical experiments are reported to confirm the theoretical analysis.

Keywords

Local multilevel algorithmAdaptive finite element methodComplex coefficientsGauss-Seidel smoother

MSC classification

Secondary: 65F10: Iterative methods for linear systems 65N30: Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
Type
Research Article
Information
Numerical Mathematics: Theory, Methods and Applications , Volume 8 , Issue 3 , August 2015 , pp. 336 - 355
Copyright
Copyright © Global-Science Press 2015 

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