A computational study of stabilized, low-order C finite element approximations of Darcy equations

We consider finite element methods for the Darcy equations that are designed to work with standard, low order C finite element spaces. Such spaces remain a popular choice in the engineering practice because they offer the convenience of simple and uniform data structures and reasonable accuracy. A consistently stabilized method [20] and a least-squares formulation [18] are compared with two new stabilized methods. The first one is an extension of a recently proposed polynomial pressure projection stabilization of the Stokes equations [5; 13]. The second one is a weighted average of a mixed and a Galerkin principles for the Darcy problem, and can be viewed as a consistent version of the classical penalty stabilization for the Stokes equations [9]. Our main conclusion is that polynomial pressure projection stabilization is a viable stabilization choice for low order C approximations of the Darcy problem.