Review of some adaptive node-movement techniques in finite-element and finite-difference solutions of partial differential equations
type: Item
instance of: scholarly article
title: Review of some adaptive node-movement techniques in finite-element and finite-difference solutions of partial differential equations
zbMATH Open document ID: 0733.65057
DOI: 10.1016/0021-9991(91)90277-R
author: N. E. Zubov
published in: Journal of Computational Physics
publication date: 1991-01-01T00:00:00Z
review text: The authors present a useful review of 116 papers devoted to grid methods with adaptive distributions of nodes. Finite-element and difference methods with such adaptations are very efficient for nonstationary problems that contain moving regions of rapid change in functions to be found. In particular, problems of hydrodynamics and gas dynamics should be mentioned. Adaptive techniques include minimization or equidistribution of the error measure integral. Methods based on attraction and repulsion pseudoforces between nodes are considered as well. In my opinion, a few important results in the field under consideration have been published by Russian authors like S. K. Godunov and others.
Mathematics Subject Classification ID: 65M50
Mathematics Subject Classification ID: 65M06
Mathematics Subject Classification ID: 65M60
Mathematics Subject Classification ID: 65-02
zbMATH DE Number: 4213355
zbMATH Keywords: research survey
zbMATH Keywords: grid methods
zbMATH Keywords: adaptive distributions of nodes
zbMATH Keywords: Finite- element
zbMATH Keywords: difference methods
zbMATH Keywords: moving regions
reviewed by: Evgeniĭ Dyakonov
describes a project that uses: GEAR
MaRDI profile type: Publication
cites work: Solutions in the large for nonlinear hyperbolic systems of equations
cites work: Boundary-fitted coordinate systems for numerical solution of partial differential equations. A review
cites work: Q3732914
cites work: Grid generation techniques in computational fluid dynamics
cites work: Progress in computational physics
cites work: Adaptive grid generation
cites work: General curvilinear coordinate systems
cites work: Stiff systems of kinetic equations - a practitioner's view
cites work: The automatic integration of ordinary differential equations
cites work: Comparing numerical methods for stiff systems of O.D.E:s
cites work: Q3686255
cites work: Error induced by coordinate systems
cites work: On the use of nonuniform grids in finite-difference equations
cites work: Relationship between the truncation errors of centered finite-difference approximations on uniform and nonuniform meshes
cites work: Generalized Coordinate Forms of Governing Fluid Equations and Associated Geometrically Induced Errors
cites work: Mesh Modification for Evolution Equations
cites work: A new method for solving two-point boundary value problems using optimal node distribution
cites work: On Selection of Equidistributing Meshes for Two-Point Boundary-Value Problems
cites work: On the Numerical Solution of Initial/Boundary-Value Problems in One Space Dimension
cites work: Campylotropic coordinates
cites work: A simple adaptive technique for nonlinear wave problems
cites work: Simple time and space adaptation in one‐dimensional evolutionary partial differential equations
cites work: Adaptive Grid Method for Problems in Fluid Mechanics and Heat Transfer
cites work: Adaptive gridding for finite difference solutions to heat and mass transfer problems
cites work: Grid adaption for problems in fluid dynamics
cites work: Q3318298
cites work: The construction of discrete orthogonal coordinates
cites work: A Simplified Moving Finite Difference Scheme: Application to Dense Gas Dispersion
cites work: High-Re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method
cites work: Idealized dynamic grid computation of physical systems
cites work: Adaptive zoning for singular problems in two dimensions
cites work: Coordinate system control: Adaptive meshes
cites work: Applications and generalizations of variational methods for generating adaptive meshes
cites work: Application of a variational method for generating adaptive grids
cites work: On some methods for the numerical simulation of flows with complex structure
cites work: Observations on an adaptive moving grid method for one-dimensional systems of partial differential equations
cites work: Generation of solution-adaptive computational grids using optimization
cites work: Grid orthogonalization for curvilinear alternating-direction techniques
cites work: Generation of computational grids using optimization
cites work: Moving Finite Elements. I
cites work: Moving Finite Elements. II
cites work: The moving finite element method: Applications to general partial differential equations with multiple large gradients
cites work: Q3696449
cites work: Q3813123
cites work: A simplified adaptive mesh technique derived from the moving finite element method
cites work: A moving Petrov-Galerkin method for transport equations
cites work: Equidistributing principles in moving finite element methods
cites work: Generalized Petrov-Galerkin methods for the numerical solution of Burgers' equation
cites work: On the Structure of the Moving Finite-element Equations
cites work: Moving finite element modelling of compressible flow
cites work: Mesh-Independent Spectra in the Moving Finite Element Equations
cites work: An Adaptive Finite Element Method for Steady and Transient Problems
cites work: Application of the finite-element method to one-dimensional flame propagation problems
cites work: Development and application of an adaptive finite element method to reaction-diffusion equations
cites work: Application of Adaptive Grids to Fluid-Flow Problems with Asymptotic Solutions
cites work: The use of solution adaptive grids in solving partial differential equations
cites work: Q3318050

Review of some adaptive node-movement techniques in finite-element and finite-difference solutions of partial differential equations (cites work)
cites work: A new self-adaptive grid method

Review of some adaptive node-movement techniques in finite-element and finite-difference solutions of partial differential equations (cites work)
cites work: A Moving Finite Element Method with Error Estimation and Refinement for One-Dimensional Time Dependent Partial Differential Equations

Review of some adaptive node-movement techniques in finite-element and finite-difference solutions of partial differential equations (cites work)
cites work: A moving-mesh finite element method with local refinement for parabolic partial differential equations

Review of some adaptive node-movement techniques in finite-element and finite-difference solutions of partial differential equations (cites work)
cites work: Adaptive mesh techniques for fronts in star formation

Review of some adaptive node-movement techniques in finite-element and finite-difference solutions of partial differential equations (cites work)
cites work: Adaptive-grid methods with asymmetric time-filtering

Review of some adaptive node-movement techniques in finite-element and finite-difference solutions of partial differential equations (cites work)
cites work: Q3790874

Review of some adaptive node-movement techniques in finite-element and finite-difference solutions of partial differential equations (cites work)
cites work: Simple adaptive grids for 1-D initial value problems

Review of some adaptive node-movement techniques in finite-element and finite-difference solutions of partial differential equations (cites work)
cites work: A vectorized, finite-volume, adaptive-grid algorithm for Navier-Stokes calculations

Review of some adaptive node-movement techniques in finite-element and finite-difference solutions of partial differential equations (cites work)
cites work: A finite-volume, adaptive grid algorithm applied to planetary entry flowfields

Review of some adaptive node-movement techniques in finite-element and finite-difference solutions of partial differential equations (cites work)
cites work: Alternating direction adaptive grid generation

Review of some adaptive node-movement techniques in finite-element and finite-difference solutions of partial differential equations (cites work)
cites work: Q3327673

Review of some adaptive node-movement techniques in finite-element and finite-difference solutions of partial differential equations (cites work)
cites work: On the stability of mesh equidistribution strategies for time-dependent partial differential equations

Review of some adaptive node-movement techniques in finite-element and finite-difference solutions of partial differential equations (full work available at URL)
full work available at URL: 0021-9991(91)90277-r

Review of some adaptive node-movement techniques in finite-element and finite-difference solutions of partial differential equations (OpenAlex ID)
OpenAlex ID: W2046961553