MIXED FINITE VOLUME METHOD FOR ELLIPTIC PROBLEMS ON NON-MATCHING MULTI-BLOCK TRIANGULAR GRIDS

This article presents a mixed finite volume method for solving second-order elliptic equations with Neumann boundary conditions. The computational domains can be decomposed into non-overlapping sub-domains or blocks and the diffusion tensors may be discontinuous across the sub-domain boundaries. We define a conforming triangular partition on each sub-domains independently, and employ the standard mixed finite volume method within each sub-domain. On the interfaces between different sun-domains, the grids are non-matching. The Robin type boundary conditions are imposed on the non-matching interfaces to enhance the continuity of the pressure and flux. Both the solvability and the first order rate of convergence for this numerical scheme are rigorously proved. Numerical experiments are provided to illustrate the error behavior of this scheme and confirm our theoretical results.