Geodesic
On space–time adaptive schemes for the numerical solution of PDEs
Margarete O. Domingues1, 2 ; Olivier Roussel3 ; Kai Schneider1, 4
1 Laboratoire de Modélisation et Simulation Numérique en Mécanique et Génie des Procédés (MSNM-GP), CNRS and Universités d'Aix-Marseille, 38, rue F. Joliot–Curie, 13451 Marseille Cedex 20, France.
2 Laboratório Associado de Computação e Matemática Aplicada (LAC), Instituto Nacional de Pesquisas Espaciais (INPE), Av. dos Astronautas, 1758, 12227-010 São José dos Campos, Brazil.
3 Institut für Technische Chemie und Polymerchemie (TCP), Universität Karlsruhe, Kaiserstr. 12, 76128 Karlsruhe, Germany.
4 Centre de Mathématiques et d'Informatique (CMI), Université de Provence, 39 rue F. Joliot–Curie, 13453 Marseille Cedex 13, France.
ESAIM. Proceedings, Tome 16 (2007), pp. 181-194.

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A fully adaptive numerical scheme for solving PDEs based on a finite volume discretization with explicit time discretization is presented. The local grid refinement is triggered by a multiresolution strategy which allows to control the approximation error in space. The costly fluxes are evaluated on the adaptive grid only. For automatic time step control a Runge–Kutta–Fehlberg method is used.
A dynamic tree data structure allows memory compression and CPU time reduction. For validation different classical test problems are computed. The gain in memory and CPU time with respect to the finite volume scheme on a regular grid is reported and demonstrates the efficiency of the new method.
DOI : 10.1051/proc:2007006

Margarete O. Domingues 1, 2 ; Olivier Roussel 3 ; Kai Schneider 1, 4

1 Laboratoire de Modélisation et Simulation Numérique en Mécanique et Génie des Procédés (MSNM-GP), CNRS and Universités d'Aix-Marseille, 38, rue F. Joliot–Curie, 13451 Marseille Cedex 20, France.
2 Laboratório Associado de Computação e Matemática Aplicada (LAC), Instituto Nacional de Pesquisas Espaciais (INPE), Av. dos Astronautas, 1758, 12227-010 São José dos Campos, Brazil.
3 Institut für Technische Chemie und Polymerchemie (TCP), Universität Karlsruhe, Kaiserstr. 12, 76128 Karlsruhe, Germany.
4 Centre de Mathématiques et d'Informatique (CMI), Université de Provence, 39 rue F. Joliot–Curie, 13453 Marseille Cedex 13, France. 
@article{EP_2007_16_a12,
     author = {Margarete O. Domingues and Olivier Roussel and Kai Schneider},
     title = {On space{\textendash}time adaptive schemes for the numerical solution of {PDEs}},
     journal = {ESAIM. Proceedings},
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     doi = {10.1051/proc:2007006},
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     url = {http://geodesic.mathdoc.fr/articles/10.1051/proc:2007006/}
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Margarete O. Domingues; Olivier Roussel; Kai Schneider. On space–time adaptive schemes for the numerical solution of PDEs. ESAIM. Proceedings, Tome 16 (2007), pp. 181-194. doi : 10.1051/proc:2007006. http://geodesic.mathdoc.fr/articles/10.1051/proc:2007006/

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