Comparison of adaptive methods for one-dimensional parabolic systems

DOI10.1016/0168-9274(95)00002-CzbMath0822.65069OpenAlexW2022959746MaRDI QIDQ1891028

Peter K. Moore

Publication date: 15 October 1995

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

Full work available at URL: https://doi.org/10.1016/0168-9274(95)00002-c

zbMATH Keywords

parabolic systemsnumerical testsadaptive methodsmethod of linesmesh refinementfinite element Galerkin methodsingly implicit collocation Runge-Kutta methods

Mathematics Subject Classification ID

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) Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs (65M50)

Related Items

A comparison of adaptive software for 1D parabolic PDEs, An implicit interpolation error-based error estimation strategy for hp-adaptivity in one space dimension, A high-order global spatially adaptive collocation method for 1-D parabolic PDEs, A comparison of preconditioners in the solution of parabolic systems in three space dimensions using DASPK and a high order finite element method, Interpolation error-based a posteriori error estimation for \(hp\)-refinement using first and second derivative jumps., An adaptive approach to solutions of Fredholm integral equations of the second kind, The impact of parameter selection on the performance of an automatic adaptive code for solving reaction-diffusion equations in three dimensions, Comparison of hp-adaptive error estimates for second order hyperbolic systems, A posteriori error estimation for $hp$-adaptivity for fourth-order equations

Uses Software

• EPDCOL
• PDECOL
• DASSL
• RODAS

Cites Work

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• Algorithm 688: EPDCOL
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• A Local Refinement Finite-Element Method for One-Dimensional Parabolic Systems