Preprint 60/2001

Time-space discretization of the nonlinear hyperbolic system u_{tt} = div (\sigma (Du) + Du_t)

Carsten Carstensen and Georg Dolzmann

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Submission date: 29. Aug. 2001
Pages: 16
published in: SIAM journal on numerical analysis, 42 (2004) 1, p. 75-89 (electronic) 
DOI number (of the published article): 10.1137/S0036142901393413
Bibtex
MSC-Numbers: 65N12, 65N15, 35G25, 73G25
Keywords and phrases: finite elements, a priori error estimates, non-linear wave equations
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Abstract:
The numerical treatment of the hyperbolic system of nonlinear wave equations with linear viscosity, tex2html_wrap_inline11, is studied for a large class of globally Lipschitz continuous functions tex2html_wrap_inline13, including non-monotone stress-strain relations. The analyzed method combines an implicit Euler scheme in time with Courant (continuous and piecewise affine) finite elements in space for general time steps with varying meshes. Explicit a priori error bounds in tex2html_wrap_inline15, tex2html_wrap_inline17, and tex2html_wrap_inline19 are established for the solutions of the fully discrete scheme.

18.07.2014, 01:40