On simple moving grid methods for one-dimensional evolutionary partial differential equations

DOI10.1016/0021-9991(88)90076-9zbMath0645.65060OpenAlexW2159108665MaRDI QIDQ1103347

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

Publication date: 1988

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

Full work available at URL: https://ir.cwi.nl/pub/1729

zbMATH Keywords

Galerkin methodBJCN instabilityBonnerot-Jamet discretizationevolutionary one-dimensional PDEgrid selectionIEL inaccuracymoving grid algorithms

Mathematics Subject Classification ID

Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs (65N50) Finite difference methods for boundary value problems involving PDEs (65N06) Partial differential equations of mathematical physics and other areas of application (35Q99) Initial value problems for linear higher-order PDEs (35G10) Higher-order parabolic equations (35K25)

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Cites Work

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• An adaptive method of lines with error control for parabolic equations of the reaction-diffusion type
• A simple adaptive technique for nonlinear wave problems
• Numerical solutions of the Eulerian equations of compressible flow by a finite element method which follows the free boundary and the interfaces
• Mesh selection for discrete solution of boundary problems in ordinary differential equations
• Moving Finite Elements. I
• Simple time and space adaptation in one‐dimensional evolutionary partial differential equations
• Space‐time finite elements incorporating characteristics for the burgers' equation
• Stability and Convergence of a Generalized Crank-Nicolson Scheme on a Variable Mesh for the Heat Equation
• On the Numerical Solution of Initial/Boundary-Value Problems in One Space Dimension
• On the Scope of the Method of Modified Equations
• A second order finite element method for the one-dimensional Stefan problem
• On a quasi-linear parabolic equation occurring in aerodynamics