MFEM: A modular finite element methods library

Finite Element Methods for Convection Diffusion Equation

This paper deals with the finite element solution of the convection diffusion equation in one and two dimensions. Two main techniques are adopted and compared. The first one includes Petrov-Galerkin based on Lagrangian tensor product elements in conjunction with streamlined upwinding. The second approach represents Bubnov/Petrov-Galerkin schemes based on a new group of exponential elements. It ...

Finite Element Methods

Mixed Finite Element Methods

A new mixed nite element method on totally distorted rectangular meshes is introduced with optimal error estimates for both pressure and velocity. This new mixed discretization ts the geometric shapes of the discontinuity of the rough coeecients and domain boundaries well. This new mixed method also enables us to derive the optimal error estimates and existence and uniqueness of Thomas's mixed ...

Adaptive Finite Element Methods

Adaptive methods are now widely used in the scientific computation to achieve better accuracy with minimum degree of freedom. In this chapter, we shall briefly survey recent progress on the convergence analysis of adaptive finite element methods (AFEMs) for second order elliptic partial differential equations and refer to Nochetto, Siebert and Veeser [14] for a detailed introduction to the theo...

Mixed Finite Element Methods

Finite element methods in which two spaces are used to approximate two different variables receive the general denomination of mixed methods. In some cases, the second variable is introduced in the formulation of the problem because of its physical interest and it is usually related with some derivatives of the original variable. This is the case, for example, in the elasticity equations, where...