A posteriori error estimator for a strongly conservative finite element method of Stokes-Darcy coupling equation

Khan, Arbaz and Kanschat, Guido (2017) A posteriori error estimator for a strongly conservative finite element method of Stokes-Darcy coupling equation. [MIMS Preprint]

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Abstract

In this paper, a posteriori error estimator for a strongly conservative finite element method will be presented for the coupling of Stokes flow with porous media flow in two dimensions. These flows are governed by Stokes and Darcy equations with the Beavers-Joseph-Saffman interface condition. We discretize using a divergence-conforming velocity space with matching pressure space (such as Raviart-Thomas spaces). A reliable and efficient residual-based a posteriori error estimator is derived for the coupled problem. Several numerical experiments are presented to validate the theoretical properties of this estimator and show the capability of the corresponding adaptive algorithm to localize the singularities of the solution.

Item Type: MIMS Preprint
Uncontrolled Keywords: a posteriori analysis; Divergence-conforming DG methods; Stokes flow; Darcy flow; Beavers-Joseph-Saffman transmissibility conditions.
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 35 Partial differential equations
MSC 2010, the AMS's Mathematics Subject Classification > 65 Numerical analysis
MSC 2010, the AMS's Mathematics Subject Classification > 76 Fluid mechanics
Depositing User: Dr Arbaz Khan
Date Deposited: 16 Sep 2017
Last Modified: 08 Nov 2017 18:18
URI: http://eprints.maths.manchester.ac.uk/id/eprint/2574

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