A comparison of some adaptive space mesh solvers for the numerical solution of parabolic partial differential equations

DOI10.1016/0898-1221(96)00009-0zbMath0853.65093OpenAlexW2061434321MaRDI QIDQ1913461

Yanyan Li

Publication date: 8 July 1996

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0898-1221(96)00009-0

zbMATH Keywords

initial value problemsfinite differencemoving finite element methodperformancesstatic regriddingadaptive space mesh solvers

Mathematics Subject Classification ID

Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Initial value problems for second-order parabolic equations (35K15) Method of lines for initial value and initial-boundary value problems involving PDEs (65M20) Complexity and performance of numerical algorithms (65Y20)

Uses Software

• PDECOL
• DASSL
• LSODE
• ODEPACK

Cites Work

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• Simple adaptive grids for 1-D initial value problems
• A moving-mesh finite element method with local refinement for parabolic partial differential equations
• 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
• Moving mesh methods based on moving mesh partial differential equations
• A Method for the Spatial Discretization of Parabolic Equations in One Space Variable
• Moving Finite Elements. I
• Note on Finite Difference Approximations to Burgers’ Equation
• A Moving Finite Element Method with Error Estimation and Refinement for One-Dimensional Time Dependent Partial Differential Equations
• Algorithm 540: PDECOL, General Collocation Software for Partial Differential Equations [D3]
• A Set of Library Routines for Solving Parabolic Equations in One Space Variable
• An Adaptive Finite Element Method for Initial-Boundary Value Problems for Partial Differential Equations
• Software for Nonlinear Partial Differential Equations
• Algorithm 731: A moving-grid interface for systems of one-dimensional time-dependent partial differential equations
• Hierarchical finite element bases for triangular and tetrahedral elements

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