Mixed finite element methods for groundwater flow in heterogeneous aquifers

Abstract

This paper is concerned with a comparison of the performance and efficiency of mixed finite element methods for solving single phase fluid flow in porous media. Particular attention is given to the accurate determination of the groundwater fluxes. The linear systems generated by the mixed finite element method (MFEM) are indefinite. Symmetric positive definite linear systems are generated through the introduction of Lagrange multipliers giving rise to the mixed hybrid finite element method (MHFEM). The convergence behaviour of the numerical approximations is investigated over a range of conductivity coefficients from heterogeneous, isotropic and diagonal to discontinuous, anisotropic and full, on both triangular and quadrilateral, structured and distorted meshes. The robustness and efficiency of various preconditioned solvers is investigated in terms of optimality with respect to both mesh size and conductivity coefficient.