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Volume 15, Issue 3
A Posteriori Error Analysis of a $P_2$-CDG Space-Time Finite Element Method for the Wave Equation

Yuling Guo & Jianguo Huang

DOI: 10.4208/nmtma.OA-2022-0012

Numer. Math. Theor. Meth. Appl., 15 (2022), pp. 662-678.

Published online: 2022-07

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  • Abstract

This paper develops a posteriori error bound for a space-time finite element method for the linear wave equation. The standard $P_l$ conforming element is used for the spatial discretization and a $P_2$-CDG method is applied for the time discretization. The essential ingredients in the a posteriori error analysis are the twice time reconstruction functions and the $C^1(J)$-smooth elliptic reconstruction, which lead to reliable a posteriori error bound in view of the energy method. As an outcome, a time adaptive algorithm is proposed with the error equidistribution strategy. Numerical experiments are reported to illustrate the performance of the a posteriori error bound and the validity of the adaptive algorithm.

  • Keywords

$P_2$-CDG, wave equations, a posteriori error estimate.

  • AMS Subject Headings

65M60, 65M15

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{NMTMA-15-662, author = {Guo , Yuling and Huang , Jianguo}, title = {A Posteriori Error Analysis of a $P_2$-CDG Space-Time Finite Element Method for the Wave Equation}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2022}, volume = {15}, number = {3}, pages = {662--678}, abstract = {

This paper develops a posteriori error bound for a space-time finite element method for the linear wave equation. The standard $P_l$ conforming element is used for the spatial discretization and a $P_2$-CDG method is applied for the time discretization. The essential ingredients in the a posteriori error analysis are the twice time reconstruction functions and the $C^1(J)$-smooth elliptic reconstruction, which lead to reliable a posteriori error bound in view of the energy method. As an outcome, a time adaptive algorithm is proposed with the error equidistribution strategy. Numerical experiments are reported to illustrate the performance of the a posteriori error bound and the validity of the adaptive algorithm.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.OA-2022-0012}, url = {http://global-sci.org/intro/article_detail/nmtma/20811.html} }
TY - JOUR T1 - A Posteriori Error Analysis of a $P_2$-CDG Space-Time Finite Element Method for the Wave Equation AU - Guo , Yuling AU - Huang , Jianguo JO - Numerical Mathematics: Theory, Methods and Applications VL - 3 SP - 662 EP - 678 PY - 2022 DA - 2022/07 SN - 15 DO - http://doi.org/10.4208/nmtma.OA-2022-0012 UR - https://global-sci.org/intro/article_detail/nmtma/20811.html KW - $P_2$-CDG, wave equations, a posteriori error estimate. AB -

This paper develops a posteriori error bound for a space-time finite element method for the linear wave equation. The standard $P_l$ conforming element is used for the spatial discretization and a $P_2$-CDG method is applied for the time discretization. The essential ingredients in the a posteriori error analysis are the twice time reconstruction functions and the $C^1(J)$-smooth elliptic reconstruction, which lead to reliable a posteriori error bound in view of the energy method. As an outcome, a time adaptive algorithm is proposed with the error equidistribution strategy. Numerical experiments are reported to illustrate the performance of the a posteriori error bound and the validity of the adaptive algorithm.

Guo , Yuling and Huang , Jianguo. (2022). A Posteriori Error Analysis of a $P_2$-CDG Space-Time Finite Element Method for the Wave Equation. Numerical Mathematics: Theory, Methods and Applications. 15 (3). 662-678. doi:10.4208/nmtma.OA-2022-0012
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