Error analysis for a monolithic discretization of coupled Darcy and Stokes problems

Type
Article

Authors
Girault, V.
Kanschat, G.
Rivière, B.

KAUST Grant Number
KUS-C1-016-04

Date
2014-01-01

Abstract
© de Gruyter 2014. The coupled Stokes and Darcy equations are approximated by a strongly conservative finite element method. The discrete spaces are the divergence-conforming velocity space with matching pressure space such as the Raviart-Thomas spaces. This work proves optimal error estimate of the velocity in the L2 norm in the domain and on the interface. Lipschitz regularity of the interface is sufficient to obtain the results.

Citation
Girault V, Kanschat G, Rivière B (2014) Error analysis for a monolithic discretization of coupled Darcy and Stokes problems. Journal of Numerical Mathematics 22. Available: http://dx.doi.org/10.1515/jnma-2014-0005.

Acknowledgements
Supported in part by the National Science Foundation through grants no. DMS-0810387 and DMS-0810422 and by the King Abdullah University of Science and Technology (KAUST) through award no. KUS-C1-016-04. Part of this research was prepared at the Institute for Mathematics and its Applications in Minneapolis. The first author was Visiting Professor at the Mathematics Department of Texas A & M University.

Publisher
Walter de Gruyter GmbH

Journal
Journal of Numerical Mathematics

DOI
10.1515/jnma-2014-0005

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