On spatial adaptivity and interpolation when using the method of lines

DOI10.1016/S0168-9274(97)00091-3zbMath0890.65102OpenAlexW2037147834WikidataQ60501333 ScholiaQ60501333MaRDI QIDQ1379045

P. J. Capon, Martin Berzins, Peter K. Jimack

Publication date: 9 February 1998

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

Full work available at URL: https://doi.org/10.1016/s0168-9274(97)00091-3

zbMATH Keywords

method of linesinterpolation errorspatial adaptivitystatic remeshing

Mathematics Subject Classification ID

Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) 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

Lod generalized trapezoidal formula schemes for parabolic differential equations in two space dimensions ⋮ Unconditionally stable C¹-cubic spline collocation method for solving parabolic equations ⋮ A comparison of adaptive software for 1D parabolic PDEs ⋮ An adaptive moving mesh method with static rezoning for partial differential equations ⋮ A high-order global spatially adaptive collocation method for 1-D parabolic PDEs ⋮ An extended trapezoidal formula for the diffusion equation ⋮ Implicit adaptive mesh refinement for 2D reduced resistive magnetohydrodynamics ⋮ An extended trapezoidal formula for the diffusion equation in two space dimensions ⋮ Linearly implicit generalized trapezoidal formulas for nonlinear differential equations ⋮ Generalized trapezoidal formulas for convection-diffusion equations ⋮ Extended one-step time-integration schemes for convection-diffusion equations ⋮ Numerical solution of the generalized Burgers' equation via spectral/spline methods ⋮ Generalized trapezoidal formulas for parabolic equations

Uses Software

• PLTMG
• SPRINT2D
• RODAS

Cites Work

• An adaptive finite element scheme for transient problems in CFD
• A \(C^ 1\) interpolant for codes based on backward differentiation formulae
• Developing software for time-dependent problems using the method of lines and differential-algebraic integrators
• A unified approach to compressible and incompressible flows
• Finite element solution of compressible viscous flows using conservative variables
• A Method for the Spatial Discretization of Parabolic Equations in One Space Variable
• Compressible viscous flow calculations using compatible finite element approximations
• Moving Finite Elements. I
• A Moving Mesh Numerical Method for Hyperbolic Conservation Laws
• Construction of Variable-Stepsize Multistep Formulas
• Temporal Derivatives in the Finite-Element Method on Continuously Deforming Grids
• ODE solvers and the method of lines
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