Journal of the
Korean Mathematical Society JKMS

We construct a symmetric finite volume element (SFVE) scheme for a self-adjoint elliptic problem on tetrahedron grids and prove that our new scheme has optimal convergent order for the solution and has superconvergent order for the flux when grids are quasi-uniform and regular. The symmetry of our scheme is helpful to solve efficiently the corresponding discrete system. Numerical experiments are carried out to confirm the theoretical results.

Keywords: symmetry, finite volume element scheme, superconvergence, tetrahedron grids

MSC numbers: Primary 65M08, 65M15, 65M12