Some user-oriented comparisons of adaptive grid methods for partial differential equations in one space dimension

DOI10.1016/S0168-9274(97)00080-9zbMath0890.65100OpenAlexW1985248902MaRDI QIDQ1379051

W. E. Schiesser, Philippe Saucez, Alain Vande Wouwer

Publication date: 6 July 1998

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0168-9274(97)00080-9

zbMATH Keywords

algorithmsmethod of linesmoving gridcomparisonslocal refinement

Mathematics Subject Classification ID

Initial value problems for second-order parabolic equations (35K15) Method of lines for initial value and initial-boundary value problems involving PDEs (65M20) Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs (65M50)

Related Items

On asymptotic global error estimation and control of finite difference solutions for semilinear parabolic equations ⋮ Linearly implicit generalized trapezoidal formulas for nonlinear differential equations ⋮ Generalized trapezoidal formulas for convection-diffusion equations ⋮ Adaptive method of lines solutions for the extended fifth-order Korteweg-de Vries equation ⋮ Highly convergent simulations of transport dynamics in organic light-emitting diodes ⋮ An adaptive method of lines solution of the Korteweg-de Vries equation

Uses Software

• DASSL
• RODAS
• MOVCOL
• Algorithm 731
• CWRESU
• CWRESX

Cites Work

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• Review of some adaptive node-movement techniques in finite-element and finite-difference solutions of partial differential equations
• A numerical study of three moving-grid methods for one-dimensional partial differential equations which are based on the method of lines
• Simple adaptive grids for 1-D initial value problems
• A simple adaptive technique for nonlinear wave problems
• Some observations on a static spatial remeshing method based on equidistribution principles
• A moving collocation method for solving time dependent partial differential equations
• Generation of Finite Difference Formulas on Arbitrarily Spaced Grids
• Simple time and space adaptation in one‐dimensional evolutionary partial differential equations
• Numerical modeling of unsteady flame propagation
• Moving Mesh Partial Differential Equations (MMPDES) Based on the Equidistribution Principle
• Analysis of Moving Mesh Partial Differential Equations with Spatial Smoothing
• Algorithm 731: A moving-grid interface for systems of one-dimensional time-dependent partial differential equations