Guaranteed computable bounds for the exact error in the finite element solution. I: One-dimensional model problem
type: Item
instance of: scholarly article
title: Guaranteed computable bounds for the exact error in the finite element solution. I: One-dimensional model problem
zbMATH Open document ID: 0936.65094
DOI: 10.1016/S0045-7825(99)00330-8
author: S. K. Gangaraj
author: Ivo Babuška
author: Theofanis Strouboulis
published in: Computer Methods in Applied Mechanics and Engineering
publication date: 2000-05-03T00:00:00Z
review text: The objective of the paper is to illustrate the concepts and the procedure to compute the bounds for the energy norm of the exact error in the finite element solution, and the exact error in any bounded linear functional. An upper bound for the global energy norm of the error is obtained by employing the exact solutions of the element residual problems. A lower bound is obtained by constructing the gap function for the solutions of element residual problems. Enhanced upper and lower bounds for the global energy norm of the error can be constructed by employing the equilibrium corrections. The approach given in the paper can be employed to obtain the bounds which are close to the energy norm of the exact error for coarse mesh and non-smooth solutions.
Mathematics Subject Classification ID: 65L70
Mathematics Subject Classification ID: 65L60
Mathematics Subject Classification ID: 65L10
Mathematics Subject Classification ID: 34B15
zbMATH DE Number: 1383978
zbMATH Keywords: finite element solution
zbMATH Keywords: error bounds
zbMATH Keywords: element-residual problems
reviewed by: Dana Petcu
MaRDI profile type: Publication
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full work available at URL: s0045-7825(99)00330-8
OpenAlex ID: W1985746135
description: scientific article; zbMATH DE number 1383978