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Volume 20, Issue 6
Absolute Stable Homotopy Finite Element Methods for Circular Arch Problem and Asymptotic Exactness Posteriori Error Estimate

Min-Fu Feng, Ping-Bing Ming & Rong-Kui Yang

J. Comp. Math., 20 (2002), pp. 653-672.

Published online: 2002-12

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  • Abstract

In this paper, HFEM is proposed to investigate the circular arch problem. Optimal error estimates are derived, some superconvergence results are established, and an asymptotic exactness posteriori error estimator is presented. In contrast with the classical displacement variational method, the optimal convergence rate for displacement is uniform to the small parameter. In contrast with classical mixed finite element methods, our results are free of the strict restriction on h (the mesh size) which is preserved by all the previous papers. Furtheremore, we introduce an asymptotic exactness posteriori error estimator based on a global superconvergence result which is discovered in this kind of problem for the first time.

  • Keywords

HFEM, arch, superconvergence, asymptotic exactness, posteriori error estimator.

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COPYRIGHT: © Global Science Press

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@Article{JCM-20-653, author = {Feng , Min-FuMing , Ping-Bing and Yang , Rong-Kui}, title = {Absolute Stable Homotopy Finite Element Methods for Circular Arch Problem and Asymptotic Exactness Posteriori Error Estimate}, journal = {Journal of Computational Mathematics}, year = {2002}, volume = {20}, number = {6}, pages = {653--672}, abstract = {

In this paper, HFEM is proposed to investigate the circular arch problem. Optimal error estimates are derived, some superconvergence results are established, and an asymptotic exactness posteriori error estimator is presented. In contrast with the classical displacement variational method, the optimal convergence rate for displacement is uniform to the small parameter. In contrast with classical mixed finite element methods, our results are free of the strict restriction on h (the mesh size) which is preserved by all the previous papers. Furtheremore, we introduce an asymptotic exactness posteriori error estimator based on a global superconvergence result which is discovered in this kind of problem for the first time.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8950.html} }
TY - JOUR T1 - Absolute Stable Homotopy Finite Element Methods for Circular Arch Problem and Asymptotic Exactness Posteriori Error Estimate AU - Feng , Min-Fu AU - Ming , Ping-Bing AU - Yang , Rong-Kui JO - Journal of Computational Mathematics VL - 6 SP - 653 EP - 672 PY - 2002 DA - 2002/12 SN - 20 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/8950.html KW - HFEM, arch, superconvergence, asymptotic exactness, posteriori error estimator. AB -

In this paper, HFEM is proposed to investigate the circular arch problem. Optimal error estimates are derived, some superconvergence results are established, and an asymptotic exactness posteriori error estimator is presented. In contrast with the classical displacement variational method, the optimal convergence rate for displacement is uniform to the small parameter. In contrast with classical mixed finite element methods, our results are free of the strict restriction on h (the mesh size) which is preserved by all the previous papers. Furtheremore, we introduce an asymptotic exactness posteriori error estimator based on a global superconvergence result which is discovered in this kind of problem for the first time.

Feng , Min-FuMing , Ping-Bing and Yang , Rong-Kui. (2002). Absolute Stable Homotopy Finite Element Methods for Circular Arch Problem and Asymptotic Exactness Posteriori Error Estimate. Journal of Computational Mathematics. 20 (6). 653-672. doi:
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