A Posteriori Error Analysis of a P2-CDG Space-Time Finite Element Method for the Wave Equation

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.