A comparison of adaptive software for 1D parabolic PDEs

DOI10.1016/j.cam.2003.12.016zbMath1052.65085OpenAlexW1994146126MaRDI QIDQ1877201

P. H. Muir, Rong Wang, Patrick Keast

Publication date: 16 August 2004

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2003.12.016

zbMATH Keywords

comparison of methodsnumerical results\(B\)-splinescollocationmesh adaptationa posteriori error estimateequidistribution principlesystems of parabolic equationsadaptive software package

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Method of lines for initial value and initial-boundary value problems involving PDEs (65M20) Numerical methods for differential-algebraic equations (65L80) Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs (65M50) Packaged methods for numerical algorithms (65Y15)

Related Items (7)

Recent Advances in Error Control B-spline Gaussian Collocation Software for PDEs ⋮ An interpolation-free ALE scheme for unsteady inviscid flows computations with large boundary displacements over three-dimensional adaptive grids ⋮ An Analysis of the Reliability of Error Control B-Spline Gaussian Collocation PDE Software ⋮ Performance analysis of error-control B-spline Gaussian collocation software for PDEs ⋮ Arbitrary Lagrangian Eulerian formulation for two-dimensional flows using dynamic meshes with edge swapping ⋮ Finite-volume solution of two-dimensional compressible flows over dynamic adaptive grids ⋮ Error control Gaussian collocation software for boundary value ODEs and 1D time-dependent PDEs

Uses Software

• BACOL
• EPDCOL
• NAG
• PDECOL
• DASSL
• nag
• MOVCOL
• COLROW
• Algorithm 731
• CWRESU
• CWRESX
• PDECHEB
• ARCELO

Cites Work

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• A high-order global spatially adaptive collocation method for 1-D parabolic PDEs
• High-order adaptive methods for parabolic systems
• The finite element method for parabolic equations. I. A posteriori error estimation
• The finite element method for parabolic equations. II. A posteriori error estimation and adaptive approach
• On simple moving grid methods for one-dimensional evolutionary partial differential equations
• An adaptive theta method for the solution of stiff and nonstiff differential equations
• A practical guide to splines
• A posteriori error estimation with finite element methods of lines for one-dimensional parabolic systems
• On spatial adaptivity and interpolation when using the method of lines
• A composite integration scheme for the numerical solution of systems of parabolic PDEs in one space dimension
• Developing software for time-dependent problems using the method of lines and differential-algebraic integrators
• Comparison of adaptive methods for one-dimensional parabolic systems
• A moving collocation method for solving time dependent partial differential equations
• FORTRAN Packages for Solving Certain Almost Block Diagonal Linear Systems by Modified Alternate Row and Column Elimination
• Moving Finite Elements. I
• Algorithm 540: PDECOL, General Collocation Software for Partial Differential Equations [D3]
• Package for Calculating with B-Splines
• Algorithm 731: A moving-grid interface for systems of one-dimensional time-dependent partial differential equations
• Algorithm 688: EPDCOL
• Algorithm 690: Chebyshev polynomial software for elliptic-parabolic systems of PDEs
• High-Order Finite Element Methods for Singularly Perturbed Elliptic and Parabolic Problems
• Interpolation error-based a posteriori error estimation for two-point boundary value problems and parabolic equations in one space dimension

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