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 - <p style="text-align: justify;">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.</p>