Numerical approximation and error control for a thermoelastic contact problem

Authors:
M. I. M. Copetti;D. A. French
Affiliations:
Laboratório de Análise Numérica e Astrofísica, Departamento de Matemática, Universidade Federal de Santa Maria, 97119-900 Santa Maria, RS, Brazil;Department of Mathematical Sciences, University of Cincinnati, Cincinnati, OH 45221, USA
Venue:
Applied Numerical Mathematics
Year:
2005

Citing 4
Cited 1

Finite element approximation to a contact problem in linear thermoelasticity

Mathematics of Computation
Computational Differential Equations

Computational Differential Equations
Finite Element Method for Elliptic Problems

Finite Element Method for Elliptic Problems
Numerical Solution of a Thermoviscoelastic Contact Problem by a Penalty Method

SIAM Journal on Numerical Analysis

Numerical solution of a two-dimensional hyperbolic transmission problem

Journal of Computational and Applied Mathematics

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Abstract

A numerical method using finite elements for the spatial discretization and the Crank-Nicolson scheme for the time stepping is applied to a partial differential equation problem involving thermoelastic contact. The Crank-Nicolson scheme is interpreted as a low order continuous Galerkin method. By exploiting the variational framework inherent in this approach, an a posteriori error estimate is derived. This estimate gives a bound on the approximation error that depends on computable quantities such as the mesh parameters, time step and numerical solution. In this paper, the a posteriori estimate is used to develop a time step refinement strategy. Several computational examples are included that demonstrate the performance of the method and validity of the estimate.