Displaying similar documents to “A Posteriori Error Estimates for Finite Volume Approximations”

A comparison of some a posteriori error estimates for fourth order problems

Segeth, Karel

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A lot of papers and books analyze analytical a posteriori error estimates from the point of view of robustness, guaranteed upper bounds, global efficiency, etc. At the same time, adaptive finite element methods have acquired the principal position among algorithms for solving differential problems in many physical and technical applications. In this survey contribution, we present and compare, from the viewpoint of adaptive computation, several recently published error estimation procedures...

Complementarity - the way towards guaranteed error estimates

Vejchodský, Tomáš

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This paper presents a review of the complementary technique with the emphasis on computable and guaranteed upper bounds of the approximation error. For simplicity, the approach is described on a numerical solution of the Poisson problem. We derive the complementary error bounds, prove their fundamental properties, present the method of hypercircle, mention possible generalizations and show a couple of numerical examples.

Goal oriented a posteriori error estimates for the discontinuous Galerkin method

Dolejší, Vít, Roskovec, Filip

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This paper is concerned with goal-oriented a posteriori error estimates for discontinous Galerkin discretizations of linear elliptic boundary value problems. Our approach combines the Dual Weighted Residual method (DWR) with local weighted least-squares reconstruction of the discrete solution. This technique is used not only for controlling the discretization error, but also to track the influence of the algebraic errors. We illustrate the performance of the proposed method by numerical...

Error Estimates with Post-Processing for Nonconforming Finite Elements

Friedhelm Schieweck (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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For a nonconforming finite element approximation of an elliptic model problem, we propose 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 is...