Displaying similar documents to “Anisotropic mesh adaption: application to computational fluid dynamics”

A finite element method on composite grids based on Nitsche’s method

Anita Hansbo, Peter Hansbo, Mats G. Larson (2003)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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In this paper we propose a finite element method for the approximation of second order elliptic problems on composite grids. The method is based on continuous piecewise polynomial approximation on each grid and weak enforcement of the proper continuity at an artificial interface defined by edges (or faces) of one the grids. We prove optimal order a priori and energy type a posteriori error estimates in 2 and 3 space dimensions, and present some numerical examples.

Guaranteed and robust error estimates for singularly perturbed reaction–diffusion problems

Ibrahim Cheddadi, Radek Fučík, Mariana I. Prieto, Martin Vohralík (2009)

ESAIM: Mathematical Modelling and Numerical Analysis

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We derive error estimates for singularly perturbed reaction–diffusion problems which yield a guaranteed upper bound on the discretization error and are fully and easily computable. Moreover, they are also locally efficient and robust in the sense that they represent local lower bounds for the actual error, up to a generic constant independent in particular of the reaction coefficient. We present our results in the framework of the vertex-centered finite volume method but their nature...

A posteriori error estimation and adaptivity in the method of lines with mixed finite elements

Jan Brandts (1999)

Applications of Mathematics

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We will investigate the possibility to use superconvergence results for the mixed finite element discretizations of some time-dependent partial differential equations in the construction of a posteriori error estimators. Since essentially the same approach can be followed in two space dimensions, we will, for simplicity, consider a model problem in one space dimension.