TY - JOUR
T1 - Error estimates for finite element approximations of a viscous wave equation
AU - Karaa, Samir
N1 - Funding Information:
This research was supported by Sultan Qaboos University under Grant IG/SCI/DOMS/09/09.
PY - 2011/7
Y1 - 2011/7
N2 - We consider a family of fully discrete finite element schemes for solving a viscous wave equation, where the time integration is based on the Newmark method. A rigorous stability analysis based on the energy method is developed. Optimal error estimates in both time and space are obtained. For sufficiently smooth solutions, it is demonstrated that the maximal error in the L 2-norm over a finite time interval converges optimally as O(h p+1+Δts), where p denotes the polynomial degree, s=1 or 2, h the mesh size, and Δt the time step.
AB - We consider a family of fully discrete finite element schemes for solving a viscous wave equation, where the time integration is based on the Newmark method. A rigorous stability analysis based on the energy method is developed. Optimal error estimates in both time and space are obtained. For sufficiently smooth solutions, it is demonstrated that the maximal error in the L 2-norm over a finite time interval converges optimally as O(h p+1+Δts), where p denotes the polynomial degree, s=1 or 2, h the mesh size, and Δt the time step.
KW - Energy method
KW - Error estimates
KW - Finite element method
KW - Viscous wave equation
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U2 - 10.1080/01630563.2011.580874
DO - 10.1080/01630563.2011.580874
M3 - Article
AN - SCOPUS:79957627326
SN - 0163-0563
VL - 32
SP - 750
EP - 767
JO - Numerical Functional Analysis and Optimization
JF - Numerical Functional Analysis and Optimization
IS - 7
ER -