Geodesic
Two local time stepping schemes for parabolic problems
Isabelle Faille1 ; Frédéric Nataf2 ; Françoise Willien1 ; Sylvie Wolf3
1 IFP, Département Mathématiques Appliquées, 1 et 4 avenue de Bois-Préau, 92852 Rueil-Malmaison, France. e-mail: isabelle.faille@ifp.fr, francoise.willien@ifp.fr
2 Laboratoire J.-L. Lions, CNRS UMR7598, Université Pierre et Marie Curie, France. e-mail: nataf@ann.jussieu.fr
3 Institut des Sciences de la Terre de Paris - CNRS UMR 7193, Université Pierre et Marie Curie, France. e-mail: sylvie.wolf@upmc.fr
ESAIM. Proceedings, Tome 29 (2009), pp. 58-72 Cet article a éte moissonné depuis la source EDP Sciences

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We present a strategy for solving time-dependent problems on grids with local refinements in time using different time steps in different regions of space. We propose two conservative approximations based on finite volume with piecewise constant projections and domain decomposition techniques. Next we present an iterative method for solving the composite-grid system that reduces to solution of standard problems with standard time stepping on the coarse and fine grids. At every step of the algorithm, conservativity is ensured. Finally, numerical results on parabolic and a two-phase flow problems illustrate the accuracy of the proposed methods.
DOI : 10.1051/proc/2009055

Isabelle Faille 1 ; Frédéric Nataf 2 ; Françoise Willien 1 ; Sylvie Wolf 3

1 IFP, Département Mathématiques Appliquées, 1 et 4 avenue de Bois-Préau, 92852 Rueil-Malmaison, France. e-mail: isabelle.faille@ifp.fr, francoise.willien@ifp.fr
2 Laboratoire J.-L. Lions, CNRS UMR7598, Université Pierre et Marie Curie, France. e-mail: nataf@ann.jussieu.fr
3 Institut des Sciences de la Terre de Paris - CNRS UMR 7193, Université Pierre et Marie Curie, France. e-mail: sylvie.wolf@upmc.fr 
@article{EP_2009_29_a5,
     author = {Isabelle Faille and Fr\'ed\'eric Nataf and Fran\c{c}oise Willien and Sylvie Wolf},
     title = {Two local time stepping schemes for parabolic problems},
     journal = {ESAIM. Proceedings},
     pages = {58--72},
     year = {2009},
     volume = {29},
     doi = {10.1051/proc/2009055},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/proc/2009055/}
}
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Isabelle Faille; Frédéric Nataf; Françoise Willien; Sylvie Wolf. Two local time stepping schemes for parabolic problems. ESAIM. Proceedings, Tome 29 (2009), pp. 58-72. doi: 10.1051/proc/2009055

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