A posteriori error estimates for mixed finite element Galerkin approximations to second order linear hyperbolic equations

Samir Karaa, Amiya K. Pani

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1 Citation (Scopus)

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(L2)-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.

Original languageEnglish
Pages (from-to)571-590
Number of pages20
JournalInternational Journal of Numerical Analysis and Modeling
Volume14
Issue number4-5
Publication statusPublished - 2017

Fingerprint

Linear Hyperbolic Equation
A Posteriori Error Estimates
Galerkin Approximation
Mixed Finite Elements
Finite Element Approximation
A Posteriori Error Analysis
A Posteriori Error Estimators
Wave equations
Second Order Equations
A Priori Estimates
Error analysis
Wave equation
Discrete-time
First-order
Norm
Context

Keywords

  • And a posteriori error estimates
  • First order implicit completely discrete scheme
  • Mixed elliptic reconstructions
  • Mixed finite element methods
  • Second order linear wave equation
  • Semidiscrete method

ASJC Scopus subject areas

  • Numerical Analysis

Cite this

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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∞(L2)-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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