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Volume 11, Issue 2
Convergence and Quasi-Optimality of an Adaptive Continuous Interior Penalty Finite Element Method

Lingxue Zhu & Zhenhua Zhou

DOI: 10.4208/aamm.OA-2018-0160

Adv. Appl. Math. Mech., 11 (2019), pp. 428-451.

Published online: 2019-01

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  • Abstract

An adaptive continuous interior penalty finite element method (ACIPFEM) for symmetric second order linear elliptic equations is considered. Convergence and quasi-optimality of the ACIPFEM are proved. Compared with the analyses for the adaptive finite element method or the adaptive interior penalty discontinuous Galerkin method, extra work is done to overcome the difficulties caused by the additional penalty term. Numerical tests are provided to verify the theoretical results and show advantages of the ACIPFEM.

  • Keywords

Continuous interior penalty finite element method, adaptive algorithm, convergence, quasi-optimality.

  • AMS Subject Headings

65N12, 65N15, 65N30, 78A40

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-11-428, author = {Zhu , Lingxue and Zhou , Zhenhua}, title = {Convergence and Quasi-Optimality of an Adaptive Continuous Interior Penalty Finite Element Method}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2019}, volume = {11}, number = {2}, pages = {428--451}, abstract = {

An adaptive continuous interior penalty finite element method (ACIPFEM) for symmetric second order linear elliptic equations is considered. Convergence and quasi-optimality of the ACIPFEM are proved. Compared with the analyses for the adaptive finite element method or the adaptive interior penalty discontinuous Galerkin method, extra work is done to overcome the difficulties caused by the additional penalty term. Numerical tests are provided to verify the theoretical results and show advantages of the ACIPFEM.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2018-0160}, url = {http://global-sci.org/intro/article_detail/aamm/12971.html} }
TY - JOUR T1 - Convergence and Quasi-Optimality of an Adaptive Continuous Interior Penalty Finite Element Method AU - Zhu , Lingxue AU - Zhou , Zhenhua JO - Advances in Applied Mathematics and Mechanics VL - 2 SP - 428 EP - 451 PY - 2019 DA - 2019/01 SN - 11 DO - http://doi.org/10.4208/aamm.OA-2018-0160 UR - https://global-sci.org/intro/article_detail/aamm/12971.html KW - Continuous interior penalty finite element method, adaptive algorithm, convergence, quasi-optimality. AB -

An adaptive continuous interior penalty finite element method (ACIPFEM) for symmetric second order linear elliptic equations is considered. Convergence and quasi-optimality of the ACIPFEM are proved. Compared with the analyses for the adaptive finite element method or the adaptive interior penalty discontinuous Galerkin method, extra work is done to overcome the difficulties caused by the additional penalty term. Numerical tests are provided to verify the theoretical results and show advantages of the ACIPFEM.

Zhu , Lingxue and Zhou , Zhenhua. (2019). Convergence and Quasi-Optimality of an Adaptive Continuous Interior Penalty Finite Element Method. Advances in Applied Mathematics and Mechanics. 11 (2). 428-451. doi:10.4208/aamm.OA-2018-0160
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