The Mixed Finite Volume Methods for Stokes Problem Based on Mini Element Pair

Abstract

. In this paper, we present and analyze MINI Mixed (cid:12)nite volume element methods (MINI-FVEM) for Stokes problem on triangular meshes. The trial spaces for velocity and pressure are chosen as MINI element pair, and the test spaces for velocity and pressure are taken as the piecewise constant function spaces on the respective dual grid. It is worth noting that the bilinear form derived from the gradient operator and the bilinear form derived from the divergence are unsymmetric. With the help of two new transformation operators, we establish the equivalence of bilinear forms for gradient operator between (cid:12)nite volume methods and (cid:12)nite element methods, and the equivalence of bilinear forms for divergence operator between (cid:12)nite volume methods and (cid:12)nite element methods, so the inf-sup conditions are obtained. By the element analysis methods, we give the positive de(cid:12)niteness of bilinear form for Laplacian operator. Based on the stability, convergence analysis of schemes are established. Numerical experiments are presented to illustrate the theoretical results.