Finite difference schemes on grids with local refinement in time and space for parabolic problems. I: Derivation, stability, and error analysis

DOI10.1007/BF02250633zbMath0721.65047OpenAlexW235856137MaRDI QIDQ2641090

Richard E. Ewing, Raytcho D. Lazarov, Panayot S. Vassilevski

Publication date: 1990

Published in: Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02250633

zbMATH Keywords

stabilityconvergenceerror analysisparabolic equationfinite difference schemesmesh refinementenergy inequalityfinite-volume method

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) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) 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 (15)

Approximation of parabolic problems on grids locally refined in time and space ⋮ A Space-Time Multiscale Mortar Mixed Finite Element Method for Parabolic Equations ⋮ Finite difference schemes on grids with local refinement in time and space for parabolic problems. I: Derivation, stability, and error analysis ⋮ On numerical artifacts in the solutions of difference problems for the wave equation on non-uniform meshes ⋮ Explicit stabilized multirate method for stiff differential equations ⋮ Space-time Petrov-Galerkin FEM for fractional diffusion problems ⋮ A finite difference scheme for two-dimensional semiconductor device of heat conduction on composite triangular grids ⋮ An implicit local time-stepping method based on cell reordering for multiphase flow in porous media ⋮ A finite difference scheme for compressible miscible displacement flow in porous media on grids with local refinement in time ⋮ Nearwell local space and time refinement in reservoir simulation ⋮ Model Reduction for Coupled Near-Well and Reservoir Models Using Multiple Space-Time Discretizations ⋮ Adaptive techniques for time-dependent problems ⋮ Finite difference schemes for two-dimensional miscible displacement flow in porous media on composite triangular grids ⋮ Interpolation finite difference schemes on grids locally refined in time ⋮ Block-centred finite difference methods on rectangular composite grids with refinement in space for parabolic equation

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