Anisotropic Wilson element with conforming 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 considered. Wilson element on anisotropic mesh is used to solve the Darcy equation on porous matrix. The existence and uniqueness of the approximation solution are obtained. Optimal error estimates in L2 and H1 norms are established independent of the regularity condition on the mesh. Numerical examples show the efficiency of the presented scheme. With the same number of nodal points, the results using Wilson element on anisotropic mesh are much better than those of the same element and Q1 element on regular mesh. Copyright © 2014 John Wiley & Sons, Ltd.