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Start Over Author "Karaa, Samir" Topic 65m15
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6. Error Estimates for Finite Element Approximations of a Viscous Wave Equation.

Author

Karaa, Samir

Subjects
*ERROR analysis in mathematics, *FINITE element method, *APPROXIMATION theory, *VISCOSITY, *NUMERICAL solutions to wave equations, *THEORY of wave motion, *STOCHASTIC convergence, *NUMERICAL integration
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 L2-norm over a finite time interval converges optimally as O(hp+1 + Δts), where p denotes the polynomial degree, s = 1 or 2, h the mesh size, and Δt the time step. [ABSTRACT FROM AUTHOR]

Published
2011
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