NDLI: A Local-in-Space-Timestep Approach to a Finite Element Discretization of the Heat Equation with a Posteriori Estimates

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Berrone, Stefano
Copyright Year	2009
Abstract	A new numerical method is presented for the heat equation with discontinuous coefficients based on a CrankNicolson scheme and a conforming finite element space discretization. In the proposed method each node of the spatial discretization may have the global timestep split into an arbitrary number of local substeps in order to pursue a local improvement of the time discretization in the regions of the spatial domain where the solution changes rapidly. This method can possibly be used together with adaptive strategies for both the space discretization and the choice of timesteps to suitably produce an efficient space-time discretizaton of the problem. Robust a posteriori upper and lower bounds of the error are proposed to attain this target. Moreover, some indications are given on how to modify the mesh, the timestep, and the number of substeps to improve the discretization.
Starting Page	3109
Ending Page	3138
Page Count	30
File Format	PDF
ISSN	00361429
DOI	10.1137/080737058
e-ISSN	10957170
Issue Number	4
Volume Number	47
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2009-09-25
Access Restriction	Subscribed
Subject Keyword	multiscale problems Equations with nonlinear operators parabolic problems Error bounds Mesh generation and refinement a posteriori error estimates local timesteps Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods space and time adaptivity
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Numerical Analysis Computational Mathematics

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