With special control volumes and finite volume element spaces,two symmetry-preserving finite volume element schemes for stationary diffusion problems are established on unstructured quadrilateral grids.

Based on a preserving-integral operator,by choosing a special control volume and linear finite element space under quadrilateral grids,a symmetric finite volume scheme for a self-adjoint elliptic boundary value problem is presented in this paper.

A kind of finite volume element scheme for one dimensional parabolic partial differential equation with initial and Dirichlet boundary condition is presented,and it is proved that the scheme has second order convergence accuracy with respect to discrete L 2 norm and discrete H 1 seminorm.

This paper presents a kind of finite volume element scheme for two-dimensional second order elliptic partial differential equations with Dirichlet boundary condition and we prove that the scheme has second order convergence accuracy with respect to discrete energy norm.

L ∞ norm estimates are obtained by a symmetric finite element method for the elliptic problem and the time dependent problem.

A mixed finite-volume finite-element method with unstructured grids is adopted to solve filtered compressible Navier-Stokes equations.