Error Estimate Of Block-Centered Finite Differences For 2-dimmensional Hyperbolic Equation

In this paper, a block centered difference scheme is presented. to a hyperbolic problem. The discrete L~2 error estimate is given on the non-uniform grids.In the first section, we demonstrate the petroleum reservoir simulation and the mathematical background of the method . And the following second order hyperbolic equation with initial boundary condition are given.The notations and lemmas of this paper are given in section two.In the third section, we give the block centered difference scheme of the second-order hyperbolic equation by introducing a first-order derivative variable u, and the solve method of the scheme is given.The second-order discrete L~2 error estimations of u and p are given insection four. The method is simple to compute as difference method and with high accuracy as mixed element method.Numerical results are given in section five.