A quadratic finite element method for solving biharmonic problems in \(\mathbb R^ n\)
type: Item
instance of: scholarly article
title: A quadratic finite element method for solving biharmonic problems in \(\mathbb R^ n\)
zbMATH Open document ID: 0617.65113
DOI: 10.1007/BF01401020
author: Vitoriano Ruas
published in: Numerische Mathematik
publication date: 1988-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/133223
review text: A family of simplicial finite element methods having the simplest possible structure is introduced to solve biharmonic problems in \({\mathbb{R}}^ n\), for n greater or equal to 3, using the primal variable. The family is inspired in the Morley triangle, which in some sense can be viewed as its member corresponding to the value \(n=2\). However all the new members are defined with the help of special degrees of freedom called parametrized. Equivalent convergence results are proven to hold for all the members of this family.
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 31B30
Mathematics Subject Classification ID: 35J40
zbMATH DE Number: 4001400
zbMATH Keywords: simplicial finite element methods
zbMATH Keywords: Morley triangle
zbMATH Keywords: convergence
zbMATH Keywords: nonconforming
zbMATH Keywords: parametrized degrees of freedom
zbMATH Keywords: biharmonic equations
MaRDI profile type: Publication
cites work: Q4073917
cites work: Q4162607
cites work: Q4082392
cites work: Some results on the curved plate bending problem solved with non- conforming finite elements
cites work: Finite element solution of 3D viscous flow problems using nonstandard degrees of freedom
cites work: Q4127946
OpenAlex ID: W2035665440
description: scientific article; zbMATH DE number 4001400