Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9511799 | Applied Numerical Mathematics | 2005 | 19 Pages |
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.
Related Topics
Physical Sciences and Engineering
Mathematics
Computational Mathematics
Authors
M.I.M. Copetti, D.A. French,