Convergence and complexity of arbitrary order adaptive mixed element methods for the Poisson equation
type: Item
instance of: scholarly article
title: Convergence and complexity of arbitrary order adaptive mixed element methods for the Poisson equation
zbMATH Open document ID: 1266.65182
published in: Science China. Mathematics
publication date: 2013-01-28T00:00:00Z
review text: The paper concerns the convergence and complexity of adaptive mixed finite element methods (FEMs) for the Poisson equation. The analysis starts with the proof of a quasi-orthogonality result and a localized upper bound for the error of nested discrete solutions. Then the authors prove an error estimate for an adaptive FEM based on the the quasi-orthogonality. Finally, the complexity is obtained using the a posteriori error estimates for the mixed FEM. The authors claim that the results can be extended to the 3D case if the argument for the discrete reliability, i.e., a local stable projection operator associated with two nested edge element spaces and a localized regular decomposition, for time-harmonic Maxwell's equations is employed.
reviewed by: Jiguang Sun
Mathematics Subject Classification ID: 65N12
Mathematics Subject Classification ID: 65N15
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 65Y20
Mathematics Subject Classification ID: 35J05
zbMATH DE Number: 6131968
zbMATH Keywords: mixed finite element methods
zbMATH Keywords: a posteriori error estimate
zbMATH Keywords: adaptive finite element method
zbMATH Keywords: convergence
zbMATH Keywords: computational complexity
zbMATH Keywords: Poisson equation
zbMATH Keywords: nested edge element spaces and a localized regular decomposition, for time-harmonic Maxwell's equations
author: Jianguo Huang
author: Yifeng Xu
MaRDI profile type: Publication
full work available at URL: s11425-012-4384-0
OpenAlex ID: W2262198896
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Convergence and complexity of arbitrary order adaptive mixed element methods for the Poisson equation (DOI)
DOI: 10.1007/S11425-012-4384-0