An Adaptive Finite Element Method for Linear Elliptic Problems

An Adaptive Finite Element Method for Linear Elliptic Problems

We propose an adaptive finite element method for linear elliptic problems based on an optimal maximum norm error estimate. The algorithm produces a sequence of successively refined meshes with a final mesh on which a given error tolerance is satisfied. In each step the refinement to be made is determined by locally estimating the size of certain derivatives of the exact solution through compute...

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...

An adaptive discontinuous finite volume method for elliptic problems

An adaptive discontinuous finite volume method is developed and analyzed in this paper. We prove that the adaptive procedure achieves guaranteed error reduction in a meshdependent energy norm and has a linear convergence rate. Numerical results are also presented to illustrate the theoretical analysis. © 2011 Elsevier B.V. All rights reserved.

An Adaptive Finite Element Method for Nonlinear Optimal Control Problems

Unified Multilevel Adaptive Finite Element Methods for Elliptic Problems

Many elliptic partial differential equations can be solved numerically with near optimal efficiency through the uses of adaptive refinement and multigrid solution techniques. It is our goal to develop a more unified approach to the combined process of adaptive refinement and multigrid solution which can be used with high order finite elements. The basic step of the refinement process is the bis...