Ivan Yotov

Mixed Finite Elements for Elliptic Problems with Tensor Coefficients as Cell-Centered Finite Differences

We present an expanded mixed finite element approximation of second-order elliptic problems containing a tensor coefficient. The mixed method is expanded in the sense that three variables are explicitly approximated, namely, the scalar unknown, the negative of its gradient, and its flux (the tensor coefficient times the negative gradient). The resulting linear system is a saddle point problem. In the case of the lowest order Raviart--Thomas elements on rectangular parallelepipeds, we approximate this expanded mixed method by incorporating certain quadrature rules. This enables us to write the system as a simple, cell-centered finite difference method requiring the solution of a sparse, positive semidefinite linear system for the scalar unknown. For a general tensor coefficient, the sparsity pattern for the scalar unknown is a 9-point stencil in two dimensions and 19 points in three dimensions. Existing theory shows that the expanded mixed method gives optimal order approximations in the

Locally Conservative Coupling of Stokes and Darcy Flows

L^2

A Multipoint Flux Mixed Finite Element Method

- and

Mixed Finite Element Methods on Nonmatching Multiblock Grids

H^{-s}

A MULTISCALE MORTAR MIXED FINITE ELEMENT METHOD

-norms (and superconvergence is obtained between the

Enhanced Cell-Centered Finite Differences for Elliptic Equations on General Geometry

L^2

Local flux mimetic finite difference methods

-projection of the scalar variable and its approximation). We show that these rates of convergence are retained for the finite difference method. If

Mortar Upscaling for Multiphase Flow in Porous Media

h

A New Generation EOS Compositional Reservoir Simulator: Part I - Formulation and Discretization

denotes the maximal mesh spacing, then the optimal rate is

Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals

O(h)