Convergence and Complexity of Adaptive Finite Element Methods for Elliptic Partial Differential Equations
Year: 2011
International Journal of Numerical Analysis and Modeling, Vol. 8 (2011), Iss. 4 : pp. 615–640
Abstract
In this paper, we study adaptive finite element approximations in a perturbation framework, which makes use of the existing adaptive finite element analysis of a linear symmetric elliptic problem. We analyze the convergence and complexity of adaptive finite element methods for a class of elliptic partial differential equations when the initial finite element mesh is sufficiently fine. For illustration, we apply the general approach to obtain the convergence and complexity of adaptive finite element methods for a nonsymmetric problem, a nonlinear problem as well as an unbounded coefficient eigenvalue problem.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2011-IJNAM-704
International Journal of Numerical Analysis and Modeling, Vol. 8 (2011), Iss. 4 : pp. 615–640
Published online: 2011-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 26
Keywords: Adaptive finite element convergence complexity eigenvalue nonlinear nonsymmetric unbounded.