Three First-Order Finite Volume Element Methods for Stokes Equations under Minimal Regularity Assumptions

Abstract

Three first-order finite volume element methods, namely, conforming, nonconforming, and discontinuous Galerkin schemes for Stokes equations, are analyzed and compared using the medius analysis. The latter analysis is based on a combination of arguments from a priori and a posteriori error analyses under no extra regularity assumptions on the weak solution. Best-approximation results for the energy norms hold in all cases and allow for comparison results up to generic equivalence constants and higher-order data oscillation of the applied volume forces with little modification for different pressure approximations. A priori and a posteriori analyses of discontinuous Galerkin finite volume element methods with SIPG, IIPG, NIPG are included for completeness.