Computable error bounds for finite element approximation on nonpolygonal domains. (18th August 2016)

• Record Type: Journal Article
• Authors: Ainsworth, Mark; Rankin, Richard
• Is Part Of: IMA journal of numerical analysis. Volume 37:Number 2(2017)
• Page Start: 604
• Page End: 645
• Publication Date: 2016-08-18
• Subjects: computable error bounds -- finite element approximation -- nonpolygonal domains.; Numerical analysis -- Periodicals; 519.405
• DOI: 10.1093/imanum/drw040
• Languages: English
• ISSNs: 0272-4979

Abstract

Abstract : We consider the case of piecewise affine approximation of the solution to the Poisson problem, with pure Neumann boundary data, on nonpolygonal domains. A computable, guaranteed upper bound on the energy norm of the error in such a finite element approximation is obtained. The estimator takes the effect of the boundary approximation into account and provides, up to a constant and oscillation terms, local lower bounds on the energy norm of the error.