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.
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