A \(C^ 1\) finite element collocation method for the equations of one- dimensional nonlinear thermoviscoelasticity
type: Item
instance of: scholarly article
title: A \(C^ 1\) finite element collocation method for the equations of one- dimensional nonlinear thermoviscoelasticity
zbMATH Open document ID: 0675.73077
DOI: 10.1016/0378-4754(89)90161-4
author: Song Jiang
published in: Mathematics and Computers in Simulation
publication date: 1989-01-01T00:00:00Z
review text: The paper deals with the solution of the equations of one-dimensional nonlinear thermoelasticity and employs a finite element collocation method at Gaussian points based on the use of a function space consisting of \(C^ 1\) piecewise polynomials of degree \(\leq r\), where \(r\geq 3\) for approximation in the space variable and a three level difference scheme for approximation in the time variable. The displacement gradient u and the temperature difference \(\theta\) are computed at each time step separately and this results in computational economy. Bounds on the error are derived. The hypotheses in the paper are more stringent than those in the scheme using the finite element method, as the approximate solutions are to satisfy the differential equations exactly at the collocation points and not in an average sense through integrals.
Mathematics Subject Classification ID: 74A15
Mathematics Subject Classification ID: 74F05
Mathematics Subject Classification ID: 74S05
Mathematics Subject Classification ID: 74B20
zbMATH DE Number: 4106420
zbMATH Keywords: existence
zbMATH Keywords: uniqueness
zbMATH Keywords: error estimates
zbMATH Keywords: finite element collocation method
zbMATH Keywords: approximate solutions
MaRDI profile type: Publication
full work available at URL: 0378-4754(89)90161-4
OpenAlex ID: W2000060158
cites work: Equivalent Norms for Sobolev Spaces
cites work: Collocation methods for parabolic partial differential equations in one space dimension
cites work: Estimates of error in finite element approximate solutions to problems in linear thermoelasticity. II. Computationally uncoupled numerical schemes
cites work: Q3890207
cites work: Q3311028
cites work: Global Smooth Solutions to the Initial-Boundary Value Problem for the Equations of One-Dimensional Nonlinear Thermoviscoelasticity
cites work: Global smooth thermomechanical processes in one-dimensional nonlinear thermoviscoelasticity
cites work: Collocation methods for parabolic equations in a single space variable. Based on C\(^1\)-piecewise-polynomial spaces
cites work: Q3747810
cites work: Analyses of Spline Collocation Methods for Parabolic and Hyperbolic Problems in Two Space Variables
cites work: Application of Method of Collocation on Lines for Solving Nonlinear Hyperbolic Problems
cites work: On a finite element method for the equations of one-dimensional nonlinear thermoviscoelasticity
cites work: A priori estimates for the solutions of difference approximations to parabolic partial differential equations
cites work: A $C^1 $ Finite Element Collocation Method for Elliptic Equations
cites work: Orthogonal Collocation for Elliptic Partial Differential Equations
description: scientific article; zbMATH DE number 4106420