An implementation of a moving finite element method
type: Item
instance of: scholarly article
title: An implementation of a moving finite element method
zbMATH Open document ID: 0598.65085
DOI: 10.1016/0021-9991(86)90090-2
author: Andrew N. Hrymak
author: Gregory J. McRae
author: Arthur W. Westerberg
published in: Journal of Computational Physics
publication date: 1986-01-01T00:00:00Z
review text: This last decade, a lot of papers are devoted to the problem of adaptive gridding procedure for systems of partial differential equations. In particular such procedures are crucial for problems discretized by finite element methods when the solutions contain steep gradients. This paper is concerned with the moving finite element method (MFEM) when applied to one-dimensional spatial problem. This method is analogous to the method of lines (discretization of spatial part while the temporal part is left as a continuous operator) but in this case the spatial nodes move. It is especially suitable for parabolic or evolutionary problems where a steep front sweeps through the spatial domain. For example such methods are very interesting for combustion or oil reservoir problems, where we find phenomena with very different time scales and spatial profiles that are very steep in some regions and essentially flat in other parts of the domain. It has also been used to the solution problem. In this work, the authors i) implement directly the MFEM using a readily available integration package (LSODI); they report very good results with respect to accuracy and simulation cost, specially for Burger's equation \(u_ t=-uu_ x+\mu u_{xx},\) \(\mu =10^{-3}\), \(10^{-4}\). This equation is a simple analogue to the Navier-Stokes equations and serves as a model for many nonlinear wave propagation problems. ii) After an analysis and a review of the current MFEM literature, the authors propose a modification to the algorithm which reduces the computer time necessary to obtain an accurate solution.
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 65N40
Mathematics Subject Classification ID: 35Q99
Mathematics Subject Classification ID: 76S05
zbMATH DE Number: 3965387
zbMATH Keywords: steep gradients
zbMATH Keywords: adaptive gridding procedure
zbMATH Keywords: moving finite element method
zbMATH Keywords: combustion
zbMATH Keywords: oil reservoir
zbMATH Keywords: Burger's equation
zbMATH Keywords: nonlinear wave propagation
reviewed by: Michel Bernadou
MaRDI profile type: Publication
full work available at URL: 0021-9991(86)90090-2
OpenAlex ID: W2010094394
cites work: Q4073917
cites work: Q3956340
cites work: The moving finite element method: Applications to general partial differential equations with multiple large gradients
cites work: A moving Petrov-Galerkin method for transport equations
cites work: Generalized Petrov-Galerkin methods for the numerical solution of Burgers' equation
cites work: Unified approach to simulation on deforming elements with application to phase change problems
cites work: Moving Finite Elements. I
cites work: Moving Finite Elements. II
cites work: Q3043075
cites work: On the Structure of the Moving Finite-element Equations
cites work: Mesh-Independent Spectra in the Moving Finite Element Equations
description: scientific article; zbMATH DE number 3965387