Finite element approximation of solutions to a class of nonlinear hyperbolic-parabolic equations (Q1807703)
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scientific article; zbMATH DE number 1367793
| Language | Label | Description | Also known as |
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| English | Finite element approximation of solutions to a class of nonlinear hyperbolic-parabolic equations |
scientific article; zbMATH DE number 1367793 |
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Finite element approximation of solutions to a class of nonlinear hyperbolic-parabolic equations (English)
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25 May 2000
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The authors investigate a numerical approximation of \textit{S. S. Antman} and \textit{T. I. Seidman}'s model [J. Differ. Equations 124, No. 1, 132-185 (1996; Zbl 0844.35021)] of the longitudinal motion of a viscoelastic rod. The constitutive assumptions ensure that infinite compressive stress is necessary to produce total compression of the rod. The authors study the regularity of solution of the continuous problem, the convergence of a semi-discrete finite element method, and properties of a space-time finite element scheme. Results of sample computations are also provided.
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viscoelastic rod
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Antman-Seidman model
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numerical approximation
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infinite compressive stress
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regularity of solution
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convergence of semi-discrete finite element method
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space-time finite element scheme
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