Space-time adaptation for purely diffusive problems in an anisotropic framework. (English) Zbl 1499.65515
Summary: The main goal of this work is the proposal of an efficient space-time adaptive procedure for a cGdG approximation of an unsteady diffusion problem. We derive a suitable a posteriori error estimator where the contribution of the spatial and of the temporal discretization is kept distinct. In particular our interest is addressed to phenomena characterized by temporal multiscale as well as strong spatial directionalities. On the one hand we devise a sound criterion to update the time step, able to follow the evolution of the problem under investigation. On the other hand we exploit an anisotropic triangular adapted grid. The reliability and the efficiency of the proposed error estimator are assessed numerically.
MSC:
| 65M60 | Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs |
| 35K20 | Initial-boundary value problems for second-order parabolic equations |
| 65M50 | Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs |
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| [55] | MOX-Dipartimento di Matematica “F. Brioschi”, Politecnico di Milano, Via Bonardi 9, I-20133 Milano, Italy E-mail: stefano.micheletti@polimi.it and simona.perotto@polimi.it URL: http://www1.mate.polimi.it/∼mike/ and http://www1.mate.polimi.it/∼simona/ |
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