Error estimates for finite element approximations of a viscous wave equation

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

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+Δt s), where p denotes the polynomial degree, s=1 or 2, h the mesh size, and Δt the time step.

Original languageEnglish
Pages (from-to)750-767
Number of pages18
JournalNumerical Functional Analysis and Optimization
Volume32
Issue number7
DOIs
Publication statusPublished - Jul 2011

Fingerprint

Wave equations
Finite Element Approximation
Error Estimates
Wave equation
Newmark Method
Optimal Error Estimates
Polynomials
Energy Method
Smooth Solution
Time Integration
Stability Analysis
Mesh
Finite Element
Denote
Converge
Norm
Interval
Polynomial

Keywords

  • Energy method
  • Error estimates
  • Finite element method
  • Viscous wave equation

ASJC Scopus subject areas

  • Analysis
  • Control and Optimization
  • Signal Processing
  • Computer Science Applications

Cite this

Error estimates for finite element approximations of a viscous wave equation. / Karaa, Samir.

In: Numerical Functional Analysis and Optimization, Vol. 32, No. 7, 07.2011, p. 750-767.

Research output: Contribution to journalArticle

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