NDLI: Error Analysis of a Second-Order Locally Implicit Method for Linear Maxwell's Equations

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Sturm, Andreas Hochbruck, Marlis
Copyright Year	2016
Abstract	In this paper we consider the full discretization of linear Maxwell's equations on spatial grids which are locally refined. For such problems, explicit time integration schemes become inefficient because the smallest mesh width results in a strict CFL condition. Recently locally implicit time integration methods have become popular in overcoming the problem of so-called grid-induced stiffness. Various such schemes have been proposed in the literature and have been shown to be very efficient. However, a rigorous analysis of such methods is still lacking. In fact, the available literature focuses on error bounds which are valid on a fixed spatial mesh only but deteriorate in the limit where the smallest spatial mesh size tends to zero. Moreover, some important questions cannot be answered without such an analysis. For example, there has been no study of which elements of the spatial mesh enter the CFL condition. In this paper we provide such a rigorous analysis for a locally implicit scheme proposed by Verwer [BIT, 51 (2011), pp. 427--445] based on a variational formulation and energy techniques.
Sponsorship	Deutsche Forschungsgemeinschaft
Starting Page	3167
Ending Page	3191
Page Count	25
File Format	PDF
ISSN	00361429
DOI	10.1137/15M1038037
e-ISSN	10957170
Issue Number	5
Volume Number	54
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2016-10-27
Access Restriction	Subscribed
Subject Keyword	discontinuous Galerkin finite elements Stability and convergence of numerical methods component splitting error analysis Error bounds Equations with linear operators time integration locally implicit methods Maxwell's equations energy techniques Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods evolution equations
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Numerical Analysis Computational Mathematics

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