Numerical solution of an inverse problem of filtration

A numerical method is suggested to solve the multidimensional inverse problem for the fluid flow in a porous media in order to determine the flow rates by the given bottomhole pressure. Approximation by space is based on the finite element method that allows simulation in unstructured grids with refinement near the location of wells. Discretization by time is performed with the use of implicit difference approximation. The numerical results for two- and three-dimensional test problems are presented.