TY - JOUR
T1 - A Posteriori Error Estimates for Mixed Finite Element Galerkin Approximations to Second Order Linear Hyperbolic Equations
AU - Samir Karaa & Amiya K. Pani
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 - <p style="text-align: justify;">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&#39;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.</p>