An adaptive moving grid method for one-dimensional systems of partial differential equations

DOI10.1016/0021-9991(89)90058-2zbMath0675.65098OpenAlexW2144774510MaRDI QIDQ1122339

Joke G. Blom, Jan G. Verwer, Jesús María Sanz-Serna

Publication date: 1989

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://ir.cwi.nl/pub/1682

zbMATH Keywords

Lagrangian methodNumerical experimentsfully adaptive moving grid method

Mathematics Subject Classification ID

Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Difference operators (39A70) Finite difference methods for boundary value problems involving PDEs (65N06) Initial value problems for higher-order hyperbolic equations (35L30)

Related Items

On the convergence on nonrectangular grids, A moving collocation method for solving time dependent partial differential equations, Supraconvergence of a class of moving grid methods for solving a nonlinear problem, A note on the effect of artificial viscosity on solutions of conservation laws, An adaptive moving mesh method for two-dimensional thin film flow equations with surface tension, A study of moving mesh methods applied to a thin flame propagating in a detonator delay element, A numerical study of three moving-grid methods for one-dimensional partial differential equations which are based on the method of lines, A static-regridding method for two-dimensional parabolic partial differential equations, Iterative schemes and algorithms for adaptive grid generation in one dimension, An adaptive moving mesh method for thin film flow equations with surface tension, Optimal moving grids for time-dependent partial differential equations, An evaluation of the gradient-weighted moving-finite-element method in one space dimension, On the numerical solution of one-dimensional PDEs using adaptive methods based on equidistribution, An \(hr\)-adaptive method for the cubic nonlinear Schrödinger equation, A moving grid algorithm for a heat exchanger with phase changes, The second-order initial/boundary value problem: supraconvergence of regridding methods, Hermite collocation solution of near-singular problems using numerical coordinate transformations based on adaptivity

Uses Software

• NAG
• nag

Cites Work

• Convergence of method of lines approximations to partial differential equations
• An adaptive method of lines with error control for parabolic equations of the reaction-diffusion type
• Simple adaptive grids for 1-D initial value problems
• Observations on an adaptive moving grid method for one-dimensional systems of partial differential equations
• On simple moving grid methods for one-dimensional evolutionary partial differential equations
• A simple adaptive technique for nonlinear wave problems
• Moving Finite Elements. I
• Moving Finite Elements. II
• Fully Adaptive Solutions of One-Dimensional Mixed Initial-Boundary Value Problems with Applications to Unstable Problems in Combustion
• A Moving Finite Element Method with Error Estimation and Refinement for One-Dimensional Time Dependent Partial Differential Equations
• Simple time and space adaptation in one‐dimensional evolutionary partial differential equations
• On the Numerical Solution of Initial/Boundary-Value Problems in One Space Dimension
• On the Convergence of Iterated Remeshing
• A second order finite element method for the one-dimensional Stefan problem
• Unnamed Item
• Unnamed Item
• Unnamed Item