Numerical approximation and error control for a thermoelastic contact problem |
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Institution: | 1. Department of Engineering, University of Palermo, Viale delle Scienze, Edificio 8, Palermo, 90128, Italy;2. Center for Computational Sciences and Engineering (CCSE), Lawrence Berkeley National Laboratory MS, 50A-3111, 1 Cyclotron Rd, Berkeley, 94720, CA, United States |
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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. |
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