We present the development of a two-dimensional Mixed-Hybrid Finite Element (MHFE) model for the solution of the nonlinear equation of variably saturated ow in groundwater on unstructured triangular meshes. By this approach the Darcy velocity is approximated using lowest order Raviart-Thomas (RT 0) elements and is \exactly" mass-conserving. Hybridization is used to overcome the ill-conditioning...

In Part I of this work, we analyzed superconvergence for piecewise linear finite element approximations on triangular meshes satisfying an O(h2) approximate parallelogram property. In this work, we consider superconvergence for general unstructured but shape regular meshes. We develop a postprocessing gradient recovery scheme for the finite element solution uh, inspired in part by the smoothing...

In this work, we present a two-dimensional mixed-hybrid nite element model of variably saturated ow on unstructured triangular meshes. Velocities are approximated using lowest order Raviart-Thomas (RT 0) elements with piecewise constant pressure. The resulting nonlinear systems of algebraic equations are solved using Picard or Newton iterations. Theroretical superconvergence properties of the R...

A new algorithm for the generation of anisotropic, unstructured triangular meshes in two dimensions is described. Inputs to the algorithm are the boundary geometry and a metric that specifies the desired element size and shape as a function of position. The algorithm is an example of what we call pliant mesh generation. It first constructs the constrained Delaunay triangulation of the domain, t...

Locally or adaptively refined meshes have been successfully applied to simulation applications involving multi-scale phenomena in the geosciences. In particular, for situations with complex geometries or domain boundaries, meshes with triangular or tetrahedral cells demonstrate their superior ability to accurately represent relevant realistic features. On the other hand, these methods require m...

Classical facet elements do not provide an optimal rate of convergence of the numerical solution toward the solution of the exact problem in H(div)-norm for general unstructured meshes containing hexahedra and prisms. We propose two new families of high-order elements for hexahedra, triangular prisms and pyramids that recover the optimal convergence. These elements have compatible restrictions ...