Displaying similar documents to “Implicit a posteriori error estimation using patch recovery techniques”

Error estimation and adaptivity for nonlinear FE analysis

Antonio Huerta, Antonio Rodríguez-Ferran, Pedro Díez (2002)

International Journal of Applied Mathematics and Computer Science

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An adaptive strategy for nonlinear finite-element analysis, based on the combination of error estimation and h-remeshing, is presented. Its two main ingredients are a residual-type error estimator and an unstructured quadrilateral mesh generator. The error estimator is based on simple local computations over the elements and the so-called patches. In contrast to other residual estimators, no flux splitting is required. The adaptive strategy is illustrated by means of a complex nonlinear...

Residual and hierarchical a posteriori error estimates for nonconforming mixed finite element methods

Linda El Alaoui, Alexandre Ern (2004)

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

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We analyze residual and hierarchical a posteriori error estimates for nonconforming finite element approximations of elliptic problems with variable coefficients. We consider a finite volume box scheme equivalent to a nonconforming mixed finite element method in a Petrov–Galerkin setting. We prove that all the estimators yield global upper and local lower bounds for the discretization error. Finally, we present results illustrating the efficiency of the estimators, for instance, in the...

A posteriori error estimates with post-processing for nonconforming finite elements

Friedhelm Schieweck (2002)

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

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For a nonconforming finite element approximation of an elliptic model problem, we propose a posteriori error estimates in the energy norm which use as an additive term the “post-processing error” between the original nonconforming finite element solution and an easy computable conforming approximation of that solution. Thus, for the error analysis, the existing theory from the conforming case can be used together with some simple additional arguments. As an essential point, the property...

New results concerning the DWR method for some nonconforming FEM

Reiner Vanselow (2012)

Applications of Mathematics

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This paper presents a unified framework for the dual-weighted residual (DWR) method for a class of nonconforming FEM. Our approach is based on a modification of the dual problem and uses various ideas from literature which are combined in a new manner. The results are new error identities for some nonconforming FEM. Additionally, a posteriori error estimates with respect to the discrete H 1 -seminorm are derived.

Approximation of a nonlinear elliptic problem arising in a non-newtonian fluid flow model in glaciology

Roland Glowinski, Jacques Rappaz (2003)

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

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The main goal of this article is to establish a priori and a posteriori error estimates for the numerical approximation of some non linear elliptic problems arising in glaciology. The stationary motion of a glacier is given by a non-newtonian fluid flow model which becomes, in a first two-dimensional approximation, the so-called infinite parallel sided slab model. The approximation of this model is made by a finite element method with piecewise polynomial functions of degree 1. Numerical...

error analysis for parabolic variational inequalities

Kyoung-Sook Moon, Ricardo H. Nochetto, Tobias von Petersdorff, Chen-song Zhang (2007)

ESAIM: Mathematical Modelling and Numerical Analysis

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Motivated by the pricing of American options for baskets we consider a parabolic variational inequality in a bounded polyhedral domain Ω ⊂ ℝ d with a continuous piecewise smooth obstacle. We formulate a fully discrete method by using piecewise linear finite elements in space and the backward Euler method in time. We define an error estimator and show that it gives an upper bound for the error in (Ω)). The error estimator is localized in the sense that the size of the elliptic residual is...