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arXiv · 1002.0887

Convergence and Optimal Complexity of Adaptive Finite Element Methods

Lianhua He·Aihui Zhou
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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 prove the convergence and complexity of adaptive finite element methods for a class of elliptic partial differential equations. 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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Lianhua He, Aihui Zhou. 2010-02-04. Convergence and Optimal Complexity of Adaptive Finite Element Methods. https://arxiv.org/abs/1002.0887

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