Application of the multiscale finite element method to groundwater flow in heterogeneous porous media

Abstract

The multiscale finite element method is applied to flow in heterogeneous porous media with different change in coefficients in the paper. The method can efficiently capture the large scale behavior of the solution without resolving all the small scale features by constructing the multiscale finite element basis functions that are adaptive to the local property of the differential operator, which offers significant savings in CPU time and computer memory. The potential and flow rate of the two dimensional ground water flow problems with continuous change in coefficients, with gradual change in coefficients and with abrupt change in coefficients are analyzed by the multiscale finite element method and the conventional finite element method, respectively. The solutions based on the former method are much more accurate than those based on the later one with the same mesh size. The applications demonstrate the main advantages of the multiscale finite element method, i.e., significantly reducing computational effort and improving the accuracy of the solutions.