Block-centered Finite Difference And Multigrid Methods For Elliptic Problems

The elliptic partial differential equation is one of the most important mathematical models in practical engineering and physical fields.But there is obvious deficiency in using the traditional finite difference method which is based on grid subdivision.The grid dissection is required,if the precision of the discrete solution is improved,which will result in a rapid increase in computation.In order to make up for this deficiency,using block-centered finite difference and multigrid methods to solve the elliptic problems.The block-centered finite difference is the standard numerical method applied to the oil reservoir simulation to solve the elliptic partial differential equations,and the introduction of multigrid is a highly precise and efficient method for solving partial differential equations.Block-centered multigrid finite difference method is equipped with not only the calculation simplicity-advantage of the finite difference method,but also the high precision of mixed finite element method.