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 language | English |
|---|---|
| Pages (from-to) | 571-590 |
| Number of pages | 20 |
| Journal | International Journal of Numerical Analysis and Modeling |
| Volume | 14 |
| Issue number | 4-5 |
| Publication status | Published - 2017 |
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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
A posteriori error estimates for mixed finite element Galerkin approximations to second order linear hyperbolic equations. / Karaa, Samir; Pani, Amiya K.
In: International Journal of Numerical Analysis and Modeling, Vol. 14, No. 4-5, 2017, p. 571-590.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - A posteriori error estimates for mixed finite element Galerkin approximations to second order linear hyperbolic equations
AU - Karaa, Samir
AU - Pani, Amiya K.
PY - 2017
Y1 - 2017
N2 - 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.
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.
KW - And a posteriori error estimates
KW - First order implicit completely discrete scheme
KW - Mixed elliptic reconstructions
KW - Mixed finite element methods
KW - Second order linear wave equation
KW - Semidiscrete method
UR - http://www.scopus.com/inward/record.url?scp=85025066014&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85025066014&partnerID=8YFLogxK
M3 - Article
VL - 14
SP - 571
EP - 590
JO - International Journal of Numerical Analysis and Modeling
JF - International Journal of Numerical Analysis and Modeling
SN - 1705-5105
IS - 4-5
ER -