Anisotropic finite element approximation for a coupled continuum pipe-flow/Darcy model in Karst aquifers

Numerical method for a coupled continuum pipe-flow/Darcy model describing flow in porous media with an embedded conduit pipe is presented. Finite element on anisotropic mesh is applied to solve the Darcy equation on porous matrix and finite element on regular mesh is used to solve the pipe-flow equation on conduit region. The existence and uniqueness of the approximation solution are deduced. Two decoupling algorithms are given to solve the resulting coupled system of equations. Optimal error estimates in L2L2 and H1H1 norms are obtained independent of the regularity condition on the mesh. Numerical examples show the efficiency of the given method. With the same number of nodal-points, the results on anisotropic mesh are much better than the same element on regular mesh.