Displaying similar documents to “New results concerning the DWR method for some nonconforming FEM”

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

Similarity:

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...

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

Similarity:

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...

Implicit a posteriori error estimation using patch recovery techniques

Tamás Horváth, Ferenc Izsák (2012)

Open Mathematics

Similarity:

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...

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

Similarity:

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...

estimates for the Cahn–Hilliard equation with obstacle free energy

Ľubomír Baňas, Robert Nürnberg (2009)

ESAIM: Mathematical Modelling and Numerical Analysis

Similarity:

We derive estimates for a discretization in space of the standard Cahn–Hilliard equation with a double obstacle free energy. The derived estimates are robust and efficient, and in practice are combined with a heuristic time step adaptation. We present numerical experiments in two and three space dimensions and compare our method with an existing heuristic spatial mesh adaptation algorithm.

A posteriori error estimates for the 3 D stabilized Mortar finite element method applied to the Laplace equation

Zakaria Belhachmi (2003)

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

Similarity:

We consider a non-conforming stabilized domain decomposition technique for the discretization of the three-dimensional Laplace equation. The aim is to extend the numerical analysis of residual error indicators to this model problem. Two formulations of the problem are considered and the error estimators are studied for both. In the first one, the error estimator provides upper and lower bounds for the energy norm of the mortar finite element solution whereas in the second case, it also...

Optimal convergence and a posteriori error analysis of the original DG method for advection-reaction equations

Tie Zhu Zhang, Shu Hua Zhang (2015)

Applications of Mathematics

Similarity:

We consider the original DG method for solving the advection-reaction equations with arbitrary velocity in d space dimensions. For triangulations satisfying the flow condition, we first prove that the optimal convergence rate is of order k + 1 in the L 2 -norm if the method uses polynomials of order k . Then, a very simple derivative recovery formula is given to produce an approximation to the derivative in the flow direction which superconverges with order k + 1 . Further we consider a residual-based...