Numer. Math. Theor. Meth. Appl., 15 (2022), pp. 662-678.
Published online: 2022-07
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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} }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.