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Volume 24, Issue 2
Optimal Convergence Analysis of a Mixed Finite Element Method for Fourth-Order Elliptic Problems

Yue Yan, Weijia Li, Wenbin Chen & Yanqiu Wang

Commun. Comput. Phys., 24 (2018), pp. 510-530.

Published online: 2018-08

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  • Abstract

A Ciarlet-Raviart type mixed finite element approximation is constructed and analyzed for a class of fourth-order elliptic problems arising from solving various gradient systems. Optimal error estimates are obtained, using a super-closeness relation between the finite element solution and the Ritz projection of the PDE solution. Numerical results agree with the theoretical analysis.

  • AMS Subject Headings

65N12, 65N30, 35J30

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CiCP-24-510, author = {Yue Yan, Weijia Li, Wenbin Chen and Yanqiu Wang}, title = {Optimal Convergence Analysis of a Mixed Finite Element Method for Fourth-Order Elliptic Problems}, journal = {Communications in Computational Physics}, year = {2018}, volume = {24}, number = {2}, pages = {510--530}, abstract = {

A Ciarlet-Raviart type mixed finite element approximation is constructed and analyzed for a class of fourth-order elliptic problems arising from solving various gradient systems. Optimal error estimates are obtained, using a super-closeness relation between the finite element solution and the Ritz projection of the PDE solution. Numerical results agree with the theoretical analysis.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2017-0168}, url = {http://global-sci.org/intro/article_detail/cicp/12250.html} }
TY - JOUR T1 - Optimal Convergence Analysis of a Mixed Finite Element Method for Fourth-Order Elliptic Problems AU - Yue Yan, Weijia Li, Wenbin Chen & Yanqiu Wang JO - Communications in Computational Physics VL - 2 SP - 510 EP - 530 PY - 2018 DA - 2018/08 SN - 24 DO - http://doi.org/10.4208/cicp.OA-2017-0168 UR - https://global-sci.org/intro/article_detail/cicp/12250.html KW - Fourth-order elliptic problems, mixed finite element, optimal convergence. AB -

A Ciarlet-Raviart type mixed finite element approximation is constructed and analyzed for a class of fourth-order elliptic problems arising from solving various gradient systems. Optimal error estimates are obtained, using a super-closeness relation between the finite element solution and the Ritz projection of the PDE solution. Numerical results agree with the theoretical analysis.

Yue Yan, Weijia Li, Wenbin Chen and Yanqiu Wang. (2018). Optimal Convergence Analysis of a Mixed Finite Element Method for Fourth-Order Elliptic Problems. Communications in Computational Physics. 24 (2). 510-530. doi:10.4208/cicp.OA-2017-0168
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