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Volume 14, Issue 4-5
A Posteriori Error Estimates for Mixed Finite Element Galerkin Approximations to Second Order Linear Hyperbolic Equations

Samir Karaa & Amiya K. Pani

Int. J. Numer. Anal. Mod., 14 (2017), pp. 571-590.

Published online: 2017-08

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  • 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.

  • 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.

  • AMS Subject Headings

35R35, 49J40, 60G40

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-14-571, author = {Samir Karaa and Amiya K. Pani}, title = {A Posteriori Error Estimates for Mixed Finite Element Galerkin Approximations to Second Order Linear Hyperbolic Equations}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2017}, volume = {14}, number = {4-5}, pages = {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.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/10050.html} }
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 -

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.

Samir Karaa and Amiya K. Pani. (2017). A Posteriori Error Estimates for Mixed Finite Element Galerkin Approximations to Second Order Linear Hyperbolic Equations. International Journal of Numerical Analysis and Modeling. 14 (4-5). 571-590. doi:
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