Constrained \(C^0\) finite element methods for biharmonic problem
type: Item
instance of: scholarly article
title: Constrained \(C^0\) finite element methods for biharmonic problem
zbMATH Open document ID: 1259.65168
DOI: 10.1155/2012/863125
author: Rong An
author: Xuehai Huang
published in: Abstract and Applied Analysis
publication date: 2013-02-04T00:00:00Z
review text: Summary: This paper presents some constrained \(C^0\) finite element approximation methods for the biharmonic problem, which include the \(C^0\) symmetric interior penalty method, the \(C_0\) nonsymmetric interior penalty method, and the \(C^0\) nonsymmetric superpenalty method. In the finite element spaces, the \(C^1\) continuity across the interelement boundaries is obtained weakly by the constrained condition. For the \(C^0\) symmetric interior penalty method, the optimal error estimates in the broken \(H^2\) norm and in the \(L^2\) norm are derived. However, for the \(C^0\) nonsymmetric interior penalty method, the error estimate in the broken \(H^2\) norm is optimal and the error estimate in the \(L^2\) norm is suboptimal because of the lack of adjoint consistency. To obtain the optimal \(L^2\) error estimate, the \(C^0\) nonsymmetric superpenalty method is introduced and the optimal \(L^2\) error estimate is derived.
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 35J40
Mathematics Subject Classification ID: 65N15
zbMATH DE Number: 6134178
zbMATH Keywords: finite element
zbMATH Keywords: biharmonic problem
zbMATH Keywords: interior penalty method
zbMATH Keywords: error estimates
Wikidata QID: Q58696982
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2012/863125
OpenAlex ID: W1969066466
cites work: Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems
cites work: Finite Element Methods for Elliptic Equations Using Nonconforming Elements
cites work: A Priori Error Analysis for the hp-Version of the Discontinuous Galerkin Finite Element Method for the Biharmonic Equation
cites work: \(hp\)-version a priori error analysis of interior penalty discontinuous Galerkin finite element approximations to the biharmonic equation
cites work: \(hp\)-version interior penalty DGFEMs for the biharmonic equation
cites work: Nonconforming Elements in the Finite Element Method with Penalty
cites work: Q1858456
cites work: \(C^0\) interior penalty methods for fourth order elliptic boundary value problems on polygonal domains
cites work: Improved energy estimates for interior penalty, constrained and discontinuous Galerkin methods for elliptic problems. I
cites work: Q4162607
cites work: Conforming and divergence-free Stokes elements on general triangular meshes
description: scientific article; zbMATH DE number 6134178