A Quadratic Discontinuous Finite Volume Element Scheme for Stokes Problems

In this paper, we construct a quadratic discontinuous finite volume scheme for Stokes equations. Specifically, the quadratic discontinuous finite volume method (DFVM) is composed of the discontinuous Galerkin method with incomplete interior penalty term and the finite volume method. By means of special mapping, we simplify the bilinear form of DFVM and establish a relationship with that of the discontinuous Galerkin scheme, and proving the LBB condition. Then, we further rigorously prove that both the broken \(H^1\) $H^1$ norm error of the velocity and the standard \(L^2\) $L^2$ norm error of the pressure of this scheme converge to the optimal order. Numerical experiments are presented to confirm the theoretical results.