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.

  • Keywords

Fourth-order elliptic problems, mixed finite element, optimal convergence.

  • AMS Subject Headings

65N12, 65N30, 35J30

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CiCP-24-510, author = {}, 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 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 & Yanqiu Wang. (2020). 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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