Mixed virtual volume methods for elliptic problems

We develop a class of mixed virtual volume methods for elliptic problems on polygonal/polyhedral grids. Unlike the element introduced in [22], [13], our are reduced to symmetric, positive definite primary variable without using Lagrangian multipliers. start from usual way changing given equation into system Darcy's law, u=−K∇p. By integrating equations with some judiciously chosen test spaces each element, we define new all orders. show that these schemes equivalent nonconforming primal p. Once is computed solving system, degrees freedom Darcy velocity locally computed. Also, L2-projection onto polynomial space easy compute. Hence work opens an compute For lowest order case, give formula Raviart-Thomas like representation which satisfies conservation law. An optimal error analysis carried out and numerical results presented support theory.