Recent experiences with error estimation and adaptivity. II: Error estimation for \(h\)-adaptive approximations on grids of triangles and quadrilaterals
type: Item
instance of: scholarly article
title: Recent experiences with error estimation and adaptivity. II: Error estimation for \(h\)-adaptive approximations on grids of triangles and quadrilaterals
zbMATH Open document ID: 0782.65127
DOI: 10.1016/0045-7825(92)90090-7
author: K. A. Haque
author: Theofanis Strouboulis
published in: Computer Methods in Applied Mechanics and Engineering
publication date: 1993-04-01T00:00:00Z
review text: In part I [ibid. 97, No. 3, 399-436 (1992; Zbl 0764.65064)] residual and flux projection error estimators were presented for the finite element approximations of the solution of the Poisson equation. In the present part further numerical experiments are presented including error estimators for the vector-valued problem of plane elastostatics. A detailed numerical study of several flux-projectors for \(h\)-adaptive grids of bilinear and biquadratic quadrilaterals is conducted. A flux equilibration iteration, which may be employed in some cases to improve flux projection estimates is also included. For the case of grids of quadrilaterals, several versions of the boundary integral term in the definition of the local problems are compared. The numerical experiments confirm the good overall performance of residual estimates, and indicate that flux projection estimates in some interesting situation may be divergent.
Mathematics Subject Classification ID: 65N15
Mathematics Subject Classification ID: 74S05
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 35J05
zbMATH DE Number: 146811
zbMATH Keywords: adaptive grid
zbMATH Keywords: flux iteration
zbMATH Keywords: Poisson equation
zbMATH Keywords: error estimators
zbMATH Keywords: plane elastostatics
zbMATH Keywords: flux projection
zbMATH Keywords: numerical experiments
reviewed by: Jiří Vaníček
MaRDI profile type: Publication
full work available at URL: 0045-7825(92)90090-7
OpenAlex ID: W2050725442
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description: scientific article; zbMATH DE number 146811