Unconditional superconvergence analysis for nonlinear parabolic equation with \(EQ_1^{rot}\) nonconforming finite element
type: Item
instance of: scholarly article
title: Unconditional superconvergence analysis for nonlinear parabolic equation with \(EQ_1^{rot}\) nonconforming finite element
zbMATH Open document ID: 1368.65162
author: Junjun Wang
author: Fengna Yan
author: Dongyang Shi
published in: Journal of Scientific Computing
publication date: 2017-03-02T00:00:00Z
review text: This paper studies the unconditional superconvergence analysis for a nonlinear parabolic equation on a bounded domain with a linearised Galerkin finite element method with \(EQ^{rot}_1\) nonconforming elements. Via a time-discretised system the error is split into a temporal and spatial component. The authors obtain the superclose result of \(u\) in the broken \(H^1\)-norm due to the two special characteristic of the nonconforming \(EQ^{rot}_1\) elements. The first characteristic is that the associated finite element (FE) interpolation operator is identical to the traditional Ritz projection; the second is that the consistency error can be bounded by order \(O(h^2)\) (one order higher than the interpolation error) when the exact solution of the problem belongs to \(H^3(\Omega)\) where \(\Omega\) is the relevant domain. Furthermore, a different strategy is employed to reach the order of \(O(h^2 + \tau^2)\) rather than \(O(h + \tau^2)\) as per previous works. The analysis presented herein may be employed for other nonconforming FEs possessing the above two properties.
Mathematics Subject Classification ID: 65M12
Mathematics Subject Classification ID: 65M60
Mathematics Subject Classification ID: 35K55
Mathematics Subject Classification ID: 65M15
zbMATH DE Number: 6690795
zbMATH Keywords: nonlinear parabolic equation
zbMATH Keywords: temporal error and spatial error
zbMATH Keywords: \(EQ^{rot}_1\) nonconforming FEM
zbMATH Keywords: unconditionally
zbMATH Keywords: superclose result
reviewed by: Charis Harley
MaRDI profile type: Publication
full work available at URL: s10915-016-0243-4
OpenAlex ID: W2467378457
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DOI: 10.1007/S10915-016-0243-4
description: scientific article; zbMATH DE number 6690795