Published

A divergence free weak virtual element method for the Stokes-Darcy problem on general meshes

Gang Wang, Feng Wang, Long Chen, and Yinnian He

Computer Methods in Applied Mechanics and Engineering, 344, 998–1020, 2019

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ABSTRACT:

This paper presents a weak virtual element method on general
meshes for the Stokes-Darcy problem with the Beavers-Joseph-Saffman
interface condition. The velocity is discretized by the H(div) virtual
element. The pressure is approximated by discontinuous piecewise
polynomials. Besides, a polynomial space on the element faces is
introduced to approximate the tangential trace of the velocity in the
Stokes equations. The velocity on the discrete level is exactly
divergence free and thus the exact mass conservation is preserved in
the discretization.  The well-posedness of the discrete problem is
proved and an a priori error estimate is derived that implies the
error for the velocity in a suitable norm does not depend on the
pressure. A series of numerical experiments are reported to illustrate
the performance of the method.