Pollution Error in the h-Version of the Finite Element Method and the Local Quality of the Recovered Derivatives.

Abstract

We showed that the error in the finite-element solution has two parts, namely, the local-error and the pollution-error and we gave methods for estimating and controlling the pollution-error in any region of interest. In this paper we will show that the control of the pollution-error is essential in order to guarantee that the derivatives obtained from local recoveries have higher accuracy than the derivatives computed directly from the finite-element solution and that this control must be more stringent than the one needed to guarantee the reliability of local a-posteriori error estimation. We give an algorithm for controlling the local and the pollution-error simultaneously, in any region of interest. We show that, when one is interested in obtaining high accuracy only in some parts of the domain, the proposed algorithm gives meshes which are much more economical than the ones obtained from the classical adaptive algorithms which control the global energy-norm of the error. (AN)

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1995
Accession Number
ADA290297

Entities

People

  • C. S. Upadhyay
  • Ivo Babuška
  • S. K. Gangaraj
  • T. Strouboulis

Organizations

  • University of Maryland

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  • Energy and Power Technologies

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  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)