Convergence and Optimal Complexity of Adaptive Finite Element Methods - Mathematics > Numerical AnalysisReport as inadecuate




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Abstract: In this paper, we study adaptive finite element approximations in aperturbation framework, which makes use of the existing adaptive finite elementanalysis of a linear symmetric elliptic problem. We prove the convergence andcomplexity of adaptive finite element methods for a class of elliptic partialdifferential equations. For illustration, we apply the general approach toobtain the convergence and complexity of adaptive finite element methods for anonsymmetric problem, a nonlinear problem as well as an unbounded coefficienteigenvalue problem.



Author: Lianhua He, Aihui Zhou

Source: https://arxiv.org/







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