A Posteriori Error Estimates for Mixed Finite Element Galerkin Approximations to Second Order Linear Hyperbolic Equations

Abstract

In this article, a posteriori error analysis for mixed finite element Galerkin approximations of second order linear hyperbolic equations is discussed. Based on mixed elliptic reconstructions and an integration tool, which is a variation of Baker's technique introduced earlier by G. Baker (SIAM J. Numer. Anal., 13 (1976), 564-576) in the context of a priori estimates for a second order wave equation, a posteriori error estimates of the displacement in $L^\u221e(L^2)$-norm for the semidiscrete scheme are derived. Finally, a first order implicit-in-time discrete scheme is analyzed and a posteriori error estimators are established.