Energy Contraction and Optimal Convergence of Adaptive Iterative Linearized Finite Element Methods

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

Adaptive Finite Element Methods for Optimal

Adaptive Finite Element Methods for Optimal Control

We develop a new approach towards error control and adaptivity for nite element discretizations in optimization problems governed by partial diierential equations. Using the Lagrangian formalism the goal is to compute stationary points of the rst-order necessary opti-mality conditions. The mesh adaptation is driven by residual-based a posteriori error estimates derived by duality arguments. Thi...

Convergence and optimality of adaptive mixed finite element methods

The convergence and optimality of adaptive mixed finite element methods for the Poisson equation are established in this paper. The main difficulty for mixed finite element methods is the lack of minimization principle and thus the failure of orthogonality. A quasi-orthogonality property is proved using the fact that the error is orthogonal to the divergence free subspace, while the part of the...