The Galerkin Finite-Element Method using bilinear basis functions (in two dimensions) offers many advantages in the numerical treatment of flow through porous media. A significant disadvantage of this approach, however, is the lack of an explicit discrete requirement of conservation of mass on mesh cells. While this shortcoming is a concern in the case of single-phase flows, it is critical in t...

Abstract. In an obstacle problems with an affine obstacle, homogeneous Dirichlet boundary conditions, and standard regularity assumptions, the Crouzeix-Raviart non-conforming finite element method (FEM) allows for linear convergence as the maximal mesh-size approaches zero. The residual-based a posteriori error analysis leads to reliable and efficient control over the error with explicit consta...