A Modified Finite Volume Method For Partial Differential With Discontinuous Coefficients

Many problems in real life can be attributed to the interface problems, for example, splicing two different materials with its own transmission rate, the complex of the same substance in different conditions, such as water and ice, the cell flowing in blood vessels and groundwater flowing through different objects, such as rocks and sponge. Interface problems relates to environmental science, physics, biology mathematics and other fields. How to solve the interface problems has become one of the essential items for real problems.The solutions of Partial differential equations used to model interface problems are often discontinuous which is not applicable for solving interface problems. The finite volume is one of the effective numerical method to solve the interface problems due to its advantage.In this paper, the modified finite volume method for solving elliptic and parabolic equations is presented. Firstly, the classical finite volume method for solving interface problems of elliptic and parabolic equations are introduced. Secondly, the solving methods of the flux function and harmonic average coefficient in the classical method are improved, in order to get a modified finite volume method. What’s more, the error and stability for modified finite volume method are analyzed. Finally, some numerical examples are showed to verify effectiveness and feasivility of our method and compared with the classic method.