On an a posteriori error analysis of mixed finite element Galerkin approximations to a second order wave equation

Abstract: In this article, a posteriori error analysis is developed for mixed finite element Galerkin approximations to a second order linear hyperbolic equation. 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{\infty}(L2)-norm for the semidiscrete scheme are derived under minimal regularity. Finally, a first order implicit-in-time discrete scheme is analyzed and a posteriori error estimators are established.