A numerical study of primal mixed finite element approximations of Darcy equations

摘要

A numerical study of several finite element approximations for the primal mixed formulation of the Darcy equations is presented. In all cases the pressure is approximated by continuous piecewise-linear functions. The difference between each scheme is in the choice of the finite element approximation space for the velocity. Numerical tests confirm the theoretical convergence of some of these schemes and we investigate the convergence properties of schemes for which theoretical results are not available. Numerical results for some 2D problems suggest that some of the new schemes provide better convergence properties for the velocity.