Convergence of Finite Element Methods for Singular Stochastic Control

Singular Function Mortar Finite Element Methods

We consider the Poisson equation with Dirichlet boundary conditions on a polygonal domain with one reentrant corner. We introduce new nonconforming finite element discretizations based on mortar techniques and singular functions. The main idea introduced in this paper is the replacement of cut-off functions by mortar element techniques on the boundary of the domain. As advantages, the new discr...

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 ...

Convergence of Adaptive Finite Element Methods

Title of dissertation: CONVERGENCE OF ADAPTIVE FINITE ELEMENT METHODS Khamron Mekchay, Doctor of Philosophy, 2005 Dissertation directed by: Professor Ricardo H. Nochetto Department of Mathematics We develop adaptive finite element methods (AFEMs) for elliptic problems, and prove their convergence, based on ideas introduced by Dörfler [7], and Morin, Nochetto, and Siebert [15, 16]. We first stud...

Adaptive Finite Element Methods with convergence rates

Reliable Finite Element Methods for Self-adjoint Singular Perturbation Problems

It is well known that the standard finite element method based on the space Vh of continuous piecewise linear functions is not reliable in solving singular perturbation problems. It is also known that the solution of a two-point boundary-value singular perturbation problem admits a decomposition into a regular part and a finite linear combination of explicit singular functions. Taking into acco...