Numerical solution of quenching problems using mesh-dependent variable temporal steps

DOI10.1016/j.apnum.2006.07.018zbMath1113.76064OpenAlexW2066174411MaRDI QIDQ881499

Kewei Liang, Ping Lin, Roger C. E. Tan

Publication date: 30 May 2007

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

Full work available at URL: https://doi.org/10.1016/j.apnum.2006.07.018

zbMATH Keywords

singularityimplicit finite difference schemeadaptive method

Mathematics Subject Classification ID

Flows in porous media; filtration; seepage (76S05) Finite difference methods applied to problems in fluid mechanics (76M20) Gas dynamics (general theory) (76N15)

Related Items (9)

Numerical quenching for a semilinear parabolic equation with nonlinear boundary conditions ⋮ Adaptive ADI difference solution of quenching problems based on the 3D convection-reaction-diffusion equation ⋮ A nonconventional stability approach for a nonlinear Crank-Nicolson method solving degenerate Kawarada problems ⋮ An endeavor from the Glowinski-Le Tallec splitting for approximating the solution of Kawarada equation ⋮ On quenching for some parabolic problems with combined power-type nonlinearities ⋮ A preservative splitting approximation of the solution of a variable coefficient quenching problem ⋮ Numerical quenching for the semilinear heat equation with a singular absorption ⋮ Numerical quenching of a system of equations coupled at the boundary ⋮ Adaptive decomposition finite difference methods for solving singular problems -- a review

Uses Software

• AMRCLAW

Cites Work

• Continuous data dependence, regularization, and a three lines theorem for the heat equation with data in a space-like direction
• A numerical study of three moving-grid methods for one-dimensional partial differential equations which are based on the method of lines
• Numerical solutions to one-dimensional problems of thermoelastic contact
• On solutions of initial -boundary problem for \(u_t=u_{xx}+1/(1-u)\)
• An \(r\)-adaptive finite element method based upon moving mesh PDEs
• An adaptive Rothe method for nonlinear reaction-diffusion systems
• Quenching, nonquenching, and beyond quenching for solution of some parabolic equations
• A splitting moving mesh method for reaction-diffusion equations of quenching type
• Existence of solutions of quenching problems
• A finite difference scheme with arbitrary mesh systems for solving high-order partial differential equations
• The finite difference method at arbitrary irregular grids and its application in applied mechanics
• An Adaptive Finite Element Method for Initial-Boundary Value Problems for Partial Differential Equations
• Adaptive Mesh Refinement Using Wave-Propagation Algorithms for Hyperbolic Systems
• Beyond quenching for singular reaction‐diffusion problems
• Solving Degenerate Reaction-Diffusion Equations via Variable Step Peaceman--Rachford Splitting
• On the Blowup of u t at Quenching
• Moving Mesh Methods for Problems with Blow-Up
• Moving mesh methods in multiple dimensions based on harmonic maps
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Numerical solution of quenching problems using mesh-dependent variable temporal steps