A comparison of a continuous and a discontinuous Galerkin methods applied to a single-phase flow problem in anisotropic porous media

A model of single-phase flow of slightly compressible liquid is studied and the discontinuous and the continuous Galerkin methods for this model are compared. After studying the results of comparison, one may make conclusion that both method produce solutions that mostly are in accord with laws of physics. However, computational costs for the continuous method are less than ones for the discontinuous method, and the discontinuous method may produce non-physical jumps in solutions on initial time layers.