Discontinuous finite volume methods for the stationary Stokes–Darcy problem

Abstract

SummaryIn this paper, we analyze discontinuous finite volume methods for the stationary Stokes–Darcy problem that models coupled fluid flow and porous media flow. The discontinuous finite volume methods are combinations of finite volume method and discontinuous Galerkin method with three interior penalty types (incomplete symmetric, nonsymmetric, and symmetric), briefly, using discontinuous functions as trial functions in the finite volume method. Optimal error estimates in brokenH1norm are obtained for the three discontinuous finite volume methods. Optimal error estimates in the standardL2norm are derived for the symmetric interior penalty discontinuous finite volume method. Numerical experiments are presented to confirm the theoretical results with non‐matching meshes across the common interface of Stokes region and Darcy region. Copyright © 2015 John Wiley & Sons, Ltd.