Geodesic
Fully adaptive multiresolution schemes for strongly degenerate parabolic equations in one space dimension
Bürger, Raimund ; Ruiz, Ricardo ; Schneider, Kai1  ; Sepúlveda, Mauricio
1 Centre de Mathématiques et d’Informatique, Université de Provence, 39 rue Joliot-Curie, 13453 Marseille Cedex 13, France.
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 42 (2008) no. 4, pp. 535-563

Voir la notice de l'article provenant de la source Numdam

We present a fully adaptive multiresolution scheme for spatially one-dimensional quasilinear strongly degenerate parabolic equations with zero-flux and periodic boundary conditions. The numerical scheme is based on a finite volume discretization using the Engquist-Osher numerical flux and explicit time stepping. An adaptive multiresolution scheme based on cell averages is then used to speed up the CPU time and the memory requirements of the underlying finite volume scheme, whose first-order version is known to converge to an entropy solution of the problem. A particular feature of the method is the storage of the multiresolution representation of the solution in a graded tree, whose leaves are the non-uniform finite volumes on which the numerical divergence is eventually evaluated. Moreover using the L 1 contraction of the discrete time evolution operator we derive the optimal choice of the threshold in the adaptive multiresolution method. Numerical examples illustrate the computational efficiency together with the convergence properties.

DOI : 10.1051/m2an:2008016
Classification : 35L65, 35R05, 65M06, 76T20
Keywords: degenerate parabolic equation, adaptive multiresolution scheme, monotone scheme, upwind difference scheme, boundary conditions, entropy solution

Bürger, Raimund  ; Ruiz, Ricardo  ; Schneider, Kai 1 ; Sepúlveda, Mauricio 

1 Centre de Mathématiques et d’Informatique, Université de Provence, 39 rue Joliot-Curie, 13453 Marseille Cedex 13, France. 
@article{M2AN_2008__42_4_535_0,
     author = {B\"urger, Raimund and Ruiz, Ricardo and Schneider, Kai and Sep\'ulveda, Mauricio},
     title = {Fully adaptive multiresolution schemes for strongly degenerate parabolic equations in one space dimension},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {535--563},
     publisher = {EDP-Sciences},
     volume = {42},
     number = {4},
     year = {2008},
     doi = {10.1051/m2an:2008016},
     mrnumber = {2437773},
     zbl = {1147.65066},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/m2an:2008016/}
}
TY  - JOUR
AU  - Bürger, Raimund
AU  - Ruiz, Ricardo
AU  - Schneider, Kai
AU  - Sepúlveda, Mauricio
TI  - Fully adaptive multiresolution schemes for strongly degenerate parabolic equations in one space dimension
JO  - ESAIM: Mathematical Modelling and Numerical Analysis 
PY  - 2008
SP  - 535
EP  - 563
VL  - 42
IS  - 4
PB  - EDP-Sciences
UR  - http://geodesic.mathdoc.fr/articles/10.1051/m2an:2008016/
DO  - 10.1051/m2an:2008016
LA  - en
ID  - M2AN_2008__42_4_535_0
ER  - 
%0 Journal Article
%A Bürger, Raimund
%A Ruiz, Ricardo
%A Schneider, Kai
%A Sepúlveda, Mauricio
%T Fully adaptive multiresolution schemes for strongly degenerate parabolic equations in one space dimension
%J ESAIM: Mathematical Modelling and Numerical Analysis 
%D 2008
%P 535-563
%V 42
%N 4
%I EDP-Sciences
%U http://geodesic.mathdoc.fr/articles/10.1051/m2an:2008016/
%R 10.1051/m2an:2008016
%G en
%F M2AN_2008__42_4_535_0
Bürger, Raimund; Ruiz, Ricardo; Schneider, Kai; Sepúlveda, Mauricio. Fully adaptive multiresolution schemes for strongly degenerate parabolic equations in one space dimension. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 42 (2008) no. 4, pp. 535-563. doi: 10.1051/m2an:2008016

Cité par Sources :