  Modeling flow in geosystems with natural fault is a challenging problem due
to low permeability of fault compared to its surrounding porous media. One way
to predict the behavior of the flow while taking the effects of fault into
account is to use the mixed finite element method. However, the mixed method
could be time consuming due to large number of degree of freedom since both
pressure and velocity are considered in the system. A new modeling method is
presented in this paper. First, we introduce approximations of pressure based
on the relation of pressure and velocity. We furthure decouple the approximated
pressure from velocity so that it can be solved independently by continuous
Galerkin finite element method. The new problem involves less degree of freedom
than the mixed method for a given mesh . Moreover, local problem associated
with a small subdomain around the fault is additionally solved to increase the
accuracy of approximations around fault. Numerical experiments are conducted to
examine the accuracy and efficiency of the new method. Results of
three-dimensional tests show that our new method is up to 30$\times$ faster
than the the mixed method at given $L^2$ pressure error.
