Analysis of the MAC scheme for the three dimensional Stokes problem

In this paper, we propose a marker and cell method (MAC) with a proper quadrature scheme over non-uniform cuboid grids by using a staggered finite volume element method (FVEM) for 3D Stokes equations. The stability of the proposed MAC scheme is proven under Petrov-Galerkin method. By establishing a connection between MAC and FVEM, we rigorously prove the superconvergence property and the optimal order L2 error estimate. Finally, numerical results verify our theoretical findings.& COPY; 2023 IMACS. Published by Elsevier B.V. All rights reserved.