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Volume 8, Issue 4
Convergence and Complexity of Adaptive Finite Element Methods for Elliptic Partial Differential Equations

L. He & A. Zhou

Int. J. Numer. Anal. Mod., 8 (2011), pp. 615-640.

Published online: 2011-08

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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 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.

  • Keywords

Adaptive finite element, convergence, complexity, eigenvalue, nonlinear, nonsymmetric, unbounded.

  • AMS Subject Headings

65N15, 65N25, 65N30

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-8-615, author = {L. He and A. Zhou}, title = {Convergence and Complexity of Adaptive Finite Element Methods for Elliptic Partial Differential Equations}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2011}, volume = {8}, number = {4}, pages = {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.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/704.html} }
TY - JOUR T1 - Convergence and Complexity of Adaptive Finite Element Methods for Elliptic Partial Differential Equations AU - L. He & A. Zhou JO - International Journal of Numerical Analysis and Modeling VL - 4 SP - 615 EP - 640 PY - 2011 DA - 2011/08 SN - 8 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/704.html KW - Adaptive finite element, convergence, complexity, eigenvalue, nonlinear, nonsymmetric, unbounded. AB -

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.

L. He and A. Zhou. (2011). Convergence and Complexity of Adaptive Finite Element Methods for Elliptic Partial Differential Equations. International Journal of Numerical Analysis and Modeling. 8 (4). 615-640. doi:
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