Iterative refinement of finite element approximations for elliptic problems

Error Estimates for Finite Element Approximations of Elliptic Control Problems

We investigate finite element approximations of one-dimensional elliptic control problems. For semidiscretizations and full discretizations with piecewise constant controls we derive error estimates in the maximum norm.

An Iterative Finite Element Method for Elliptic Eigenvalue Problems

We consider the task of resolving accurately the nth eigenpair of a generalized eigenproblem rooted in some elliptic partial differential equation (PDE), using an adaptive finite element method (FEM). Conventional adaptive FEM algorithms call a generalized eigensolver after each mesh refinement step. This is not practical in our situation since the generalized eigensolver needs to calculate n e...

Mortar Finite Volume Element Approximations of Second Order Elliptic Problems

Mixed Finite Element Methods for Elliptic Problems*

This paper treats the basic ideas of mixed finite element methods at an introductory level. Although the viewpoint presented is that of a mathematician, the paper is aimed at practitioners and the mathematical prerequisites are kept to a minimum. A classification of variational principles and of the corresponding weak formulations and Galerkin methods—displacement, equilibrium, and mixed—is giv...

Analysis of a Subdomain-based Error Estimator for Finite Element Approximations of Elliptic Problems

In this artide we analyze a subdomain residual error estimator for finite element approximations of elliptic problems, It is obtained by solving local problems on patches of elements in weighted spaces and provides an upper bound on the energy norm of the error when the local problems are solved in sufficiently enriched discrete spaces, A guaranteed lower bound on the elTor is also derived by a...