A Posteriori Error Estimates for Mixed Finite Element Galerkin Approximations to Second Order Linear Hyperbolic Equations
Year: 2017
International Journal of Numerical Analysis and Modeling, Vol. 14 (2017), Iss. 4-5 : pp. 571–590
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 $L^∞(L^2)$-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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2017-IJNAM-10050
International Journal of Numerical Analysis and Modeling, Vol. 14 (2017), Iss. 4-5 : pp. 571–590
Published online: 2017-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 20
Keywords: 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.