Interpolation finite difference schemes on grids locally refined in time

DOI10.1016/S0045-7825(99)00451-XzbMath0978.65078OpenAlexW2074579193WikidataQ57694669 ScholiaQ57694669MaRDI QIDQ1595366

G. I. Shishkin, Petr N. Vabishchevich

Publication date: 21 January 2002

Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0045-7825(99)00451-x

zbMATH Keywords

convergenceDirichlet problemparabolic equationlocal grid refinementfinite difference schemesinitial boundary value problem

Mathematics Subject Classification ID

Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Initial value problems for second-order parabolic equations (35K15) Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs (65M50)

Related Items (4)

Multirate Partially Explicit Scheme for Multiscale Flow Problems ⋮ Explicit stabilized multirate method for stiff differential equations ⋮ Enforcing the Courant-Friedrichs-Lewy condition in explicitly conservative local time stepping schemes ⋮ Limitations of adaptive mesh refinement techniques for singularly perturbed problems with a moving interior layer.

Cites Work

• Adaptive techniques for time-dependent problems
• Domain decomposition and parallel processing for the numerical solution of partial differential equations
• Approximation of parabolic problems on grids locally refined in time and space
• On difference schemes on grids locally refining in time
• Difference schemes with different time mesh-sizes in subdomains for solving multidimensional parabolic equations
• Finite difference schemes on grids with local refinement in time and space for parabolic problems. I: Derivation, stability, and error analysis
• Numerical Approximations to Nonlinear Conservation Laws with Locally Varying Time and Space Grids
• Simple time and space adaptation in one‐dimensional evolutionary partial differential equations
• An Adaptive Finite Element Method for Initial-Boundary Value Problems for Partial Differential Equations
• Domain Decomposition Type Iterative Techniques for Parabolic Problems on Locally Refined Grids
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