TY - JOUR T1 - A Posteriori Error Estimates for Mixed Finite Element Galerkin Approximations to Second Order Linear Hyperbolic Equations JO - International Journal of Numerical Analysis and Modeling VL - 4-5 SP - 571 EP - 590 PY - 2017 DA - 2017/08 SN - 14 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/10050.html KW - Second order linear wave equation, mixed finite element methods, mixed elliptic reconstructions, semidiscrete method, first order implicit completely discrete scheme, and a posteriori error estimates. AB -

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 $L^∞(L^2)$-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.