A discrete duality finite volume discretization of the vorticity‐velocity‐pressure stokes problem on almost arbitrary two‐dimensional grids

Abstract

We present an application of the discrete duality finite volume method to the numerical approximation of the vorticity‐velocity‐pressure formulation of the two‐dimensional Stokes equations, associated to various nonstandard boundary conditions. The finite volume method is based on the use of discrete differential operators obeying some discrete duality principles. The scheme may be seen as an extension of the classical Marker and Cell scheme to almost arbitrary meshes, thanks to an appropriate choice of degrees of freedom. The efficiency of the scheme is illustrated by numerical examples over unstructured triangular and locally refined nonconforming meshes, which confirm the theoretical convergence analysis led in the article. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 1–30, 2015