The optimal point of the gradient of finite element solution
type: Item
instance of: scholarly article
title: The optimal point of the gradient of finite element solution
zbMATH Open document ID: 0627.65108
DOI: 10.1007/BF01900611
author: Xiaofan Huang
published in: Applied Mathematics and Mechanics. (English Edition)
publication date: 1986-01-01T00:00:00Z
review text: Consider the following Dirichlet problem: \[ -(au_ x+bu_ y)_ x- (bu_ x+cu_ y)_ y+qu=f\quad in\quad \Omega,\quad u=0\quad on\quad \partial \Omega, \] where \(\Omega\) is a bounded rectangular region of \({\mathbb{R}}^ 2.\) The author extends some superconvergence results of the gradients of the solution at Gaussian points when the coefficients a, b and c are discontinuous along a piecewise straight line S in \(\Omega\). In this way, the author uses serendipity rectangular elements of degree 2 or 3.
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 65N15
Mathematics Subject Classification ID: 35J25
zbMATH DE Number: 4020396
zbMATH Keywords: finite elements
zbMATH Keywords: discontinuous coefficients
zbMATH Keywords: superconvergence
zbMATH Keywords: Gaussian points
zbMATH Keywords: serendipity rectangular elements
reviewed by: Michel Bernadou
MaRDI profile type: Publication
cites work: Q3318238
cites work: Q4142644
cites work: Superconvergence and Reduced Integration in the Finite Element Method
cites work: General Lagrange and Hermite interpolation in \(R^n\) with applications to finite element methods
cites work: Q3875490
cites work: Q4162607
cites work: Q4749150
full work available at URL: https://doi.org/10.1007/bf01900611
OpenAlex ID: W1983693711
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description: scientific article; zbMATH DE number 4020396