Recent Advances of a Posteriori Error Analysis and Adaptive Finite Element Methods
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A Posteriori Error Analysis and Adaptive Methods for Partial Differential Equations
The adaptive finite element method based on a posteriori error estimates provides a systematic way to refine or coarsen the meshes according to the local a posteriori error estimator on the elements. One of the remarkable properties of the method is that for appropriately designed adaptive finite element procedures, the meshes and the associated numerical complexity are quasi-optimal in the sen...
متن کاملEquivalent a posteriori error estimates for spectral element solutions of constrained optimal control problem in one dimension
In this paper, we study spectral element approximation for a constrained optimal control problem in one dimension. The equivalent a posteriori error estimators are derived for the control, the state and the adjoint state approximation. Such estimators can be used to construct adaptive spectral elements for the control problems.
متن کاملA posteriori $ L^2(L^2)$-error estimates with the new version of streamline diffusion method for the wave equation
In this article, we study the new streamline diffusion finite element for treating the linear second order hyperbolic initial-boundary value problem. We prove a posteriori $ L^2(L^2)$ and error estimates for this method under minimal regularity hypothesis. Test problem of an application of the wave equation in the laser is presented to verify the efficiency and accuracy of the method.
متن کاملAdaptive Finite Element Methods for Multiphysics Problems Adaptive Finite Element Methods for Multiphysics Problems
In this thesis we develop and evaluate the performance of adaptive finite element methods for multiphysics problems. In particular, we propose a methodology for deriving computable error estimates when solving unidirectionally coupled multiphysics problems using segregated finite element solvers. The error estimates are of a posteriori type and are derived using the standard framework of dual w...
متن کاملA POSTERIORI ERROR ESTIMATES OF hp-FEM FOR OPTIMAL CONTROL PROBLEMS
Finite element approximation plays an important role in the numerical methods of optimal control problems. There have been extensive theoretical and numerical studies for the finite element approximation of various optimal control problems. However the literature is too huge to even give a very brief review here. In recent years, the adaptive finite element method has been extensively investiga...
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تاریخ انتشار 2001