An adaptive multilevel approach to parabolic equations I. General theory and 1D implementation

DOI10.1016/0899-8248(90)90016-4zbMath0722.65055OpenAlexW2085401519MaRDI QIDQ3210071

Folkmar A. Bornemann

Publication date: 1990

Published in: IMPACT of Computing in Science and Engineering (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0899-8248(90)90016-4

zbMATH Keywords

finite elementsnumerical examplesHilbert spaceerror analysismultigrid methodsmultilevel methodstraveling wavevariable ordersvariable time stepsinconsistent and nonsmooth initial datalow-order single- step discretization in time with extrapolationmethod of Rothe

Mathematics Subject Classification ID

Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Initial value problems for second-order parabolic equations (35K15) Method of lines for initial value and initial-boundary value problems involving PDEs (65M20) Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs (65M55) Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs (65M50)

Related Items (10)

Time-Space Adaptive Method of Time Layers for the Advective Allen-Cahn Equation ⋮ Two-dimensional fully adaptive solutions of reaction-diffusion equations ⋮ Adaptive FEM for reaction-diffusion equations ⋮ A time-stepping DPG scheme for the heat equation ⋮ Error estimates and adaptive finite element methods ⋮ Residual based a posteriori error estimators for eddy current computation ⋮ The Reverse Method of Lines in Flexible Multibody Dynamics ⋮ Discrete transparent boundary conditions for the numerical solution of Fresnel's equation ⋮ An adaptive Rothe method for nonlinear reaction-diffusion systems ⋮ Analysis of local uniform grid refinement

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