A variable node finite element method
type: Item
instance of: scholarly article
title: A variable node finite element method
zbMATH Open document ID: 0552.65076
DOI: 10.1016/0021-9991(85)90041-5
author: M. Calvin Mosher
published in: Journal of Computational Physics
publication date: 1985-01-01T00:00:00Z
review text: A new finite element method with variable nodes for integrating partial differential equations in one space dimension is presented. The method utilizes the approximation power of piecewise polynomial functions better than a fixed-node finite element method because it distributes grid points in a nonuniform way to suit the peculiarities of the solution at each instant of time. The method uses the gradient and curvature of the approximating piecewise polynomial itself to determine the position of the nodes rather than physical properties which vary from problem to problem. The method has been implemented in a program VFE which has the exceptional feature of a variable space step as well as a variable time step. Since the method concentrates nodes in regions where small inter- nodal spacing is needed, it is very efficient in integrating equations with shock-like solutions. Finally, the method can be extended to systems of partial differential equations in one dimension and to equations in two dimensions.
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 35G30
Mathematics Subject Classification ID: 35Q99
Mathematics Subject Classification ID: 76L05
zbMATH DE Number: 3880044
zbMATH Keywords: nonlinear diffusion equations
zbMATH Keywords: Burgers' equation
zbMATH Keywords: quench front equation
zbMATH Keywords: Stefan equation
zbMATH Keywords: Hodgkin-Huxley equations
zbMATH Keywords: gas dynamics
zbMATH Keywords: finite element method
zbMATH Keywords: variable nodes
zbMATH Keywords: shock-like solutions
MaRDI profile type: Publication
full work available at URL: 0021-9991(85)90041-5
OpenAlex ID: W2120599342
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description: scientific article; zbMATH DE number 3880044