Displaying similar documents to “Zienkiewicz–Zhu error estimators on anisotropic tetrahedral and triangular finite element meshes”

Robust local problem error estimation for a singularly perturbed problem on anisotropic finite element meshes

Gerd Kunert (2001)

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

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Singularly perturbed problems often yield solutions with strong directional features, e.g. with boundary layers. Such anisotropic solutions lend themselves to adapted, anisotropic discretizations. The quality of the corresponding numerical solution is a key issue in any computational simulation. To this end we present a new robust error estimator for a singularly perturbed reaction–diffusion problem. In contrast to conventional estimators, our proposal is suitable for anisotropic finite...

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...

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...

Implicit a posteriori error estimation using patch recovery techniques

Tamás Horváth, Ferenc Izsák (2012)

Open Mathematics

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We develop implicit a posteriori error estimators for elliptic boundary value problems. Local problems are formulated for the error and the corresponding Neumann type boundary conditions are approximated using a new family of gradient averaging procedures. Convergence properties of the implicit error estimator are discussed independently of residual type error estimators, and this gives a freedom in the choice of boundary conditions. General assumptions are elaborated for the gradient...

An equilibrated residual method with a computable error approximation for a singularly perturbed reaction-diffusion problem on anisotropic finite element meshes

Sergey Grosman (2006)

ESAIM: Mathematical Modelling and Numerical Analysis

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Singularly perturbed reaction-diffusion problems exhibit in general solutions with anisotropic features, strong boundary and/or interior layers. This anisotropy is reflected in a discretization by using meshes with anisotropic elements. The quality of the numerical solution rests on the robustness of the error estimator with respect to both, the perturbation parameters of the problem and the anisotropy of the mesh. The equilibrated residual method has been shown to provide one of...