Stability and convergence of linear parabolic mixed initial-boundary value problems on nonuniform grids
type: Item
instance of: scholarly article
title: Stability and convergence of linear parabolic mixed initial-boundary value problems on nonuniform grids
zbMATH Open document ID: 0708.65084
DOI: 10.1016/0168-9274(90)90005-Z
published in: Applied Numerical Mathematics
publication date: 1990-01-01T00:00:00Z
review text: The authors investigate the stability and convergence of variable step (space and time) algorithms in the solution of one-dimensional, linear, parabolic, mixed initial-boundary value problems. At first they consider the case of fixed nonuniform grids. In this case the number and location of the grid points do not change from one time level to another. Then the authors study the general case where the number and location of the grid points can change from one time level to another. At last, they describe for an example a procedure for the adaptive selection of the grid points at each time level.
Mathematics Subject Classification ID: 65M12
Mathematics Subject Classification ID: 65M06
Mathematics Subject Classification ID: 65M20
Mathematics Subject Classification ID: 65M50
Mathematics Subject Classification ID: 35K15
zbMATH DE Number: 4164072
zbMATH Keywords: variable step stability algorithms
zbMATH Keywords: convergence
zbMATH Keywords: nonuniform grids
zbMATH Keywords: adaptive selection of the grid points
author: R. M. M. Mattheij
author: Mitchell D. Smooke
reviewed by: Michael Jung
describes a project that uses: COLSYS
MaRDI profile type: Publication
cites work: Q3909951
cites work: An Adaptive Finite Element Method for Initial-Boundary Value Problems for Partial Differential Equations
cites work: Time-dependent solution of a premixed laminar flame
cites work: Moving Finite Elements. I
cites work: Solution of burner-stabilized premixed laminar flames by boundary value methods
cites work: Fully Adaptive Solutions of One-Dimensional Mixed Initial-Boundary Value Problems with Applications to Unstable Problems in Combustion
cites work: Monotone Difference Schemes for Diffusion-Convection Problems
cites work: On the Stability of Boundary Conditions for Separable Difference Approximations to Parabolic Equations
cites work: On the Numerical Solution of Initial/Boundary-Value Problems in One Space Dimension
cites work: Stability of parabolic difference schemes in the maximum norm
full work available at URL: 0168-9274(90)90005-z
OpenAlex ID: W1992260314
description: scientific article; zbMATH DE number 4164072