Convergence of numerical schemes involving powers of the Dirac delta function
type: Item
instance of: scholarly article
title: Convergence of numerical schemes involving powers of the Dirac delta function
zbMATH Open document ID: 0691.65067
DOI: 10.1016/0022-247X(90)90439-M
author: M. Adamczewski
author: J.-F. Colombeau
author: A. Y. Le Roux
published in: Journal of Mathematical Analysis and Applications
publication date: 1990-01-01T00:00:00Z
review text: The Hull elastoplastic numerical method uses a code which has good stability properties, but involves in the case of shock waves, multiplication of distributions, typically powers of Dirac delta functions. This makes the analysis of this scheme difficult, e.g. when one is trying to improve the scheme with the use of antidiffusion techniques. Using the work of one of the authors on the nonlinear theory of distributions a rigorous approach to such problems is suggested, by which suitable modifications to improve the convergence of methods such as the Hull elastoplastic code, mentioned above, can be obtained rather by theoretical than empirical analysis.
Mathematics Subject Classification ID: 65M12
Mathematics Subject Classification ID: 76L05
Mathematics Subject Classification ID: 35L67
zbMATH DE Number: 4131578
zbMATH Keywords: Hull elastoplastic method
zbMATH Keywords: stability
zbMATH Keywords: shock waves
zbMATH Keywords: Dirac delta functions
zbMATH Keywords: nonlinear theory of distributions
zbMATH Keywords: convergence
reviewed by: Philip Brenner
MaRDI profile type: Publication
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cites work: Holomorphic generalized functions
cites work: Borel's theorem for generalized functions
cites work: Multiplications of distributions in elasticity and hydrodynamics
cites work: Q3774366
description: scientific article; zbMATH DE number 4131578