Convergence of numerical schemes involving powers of the Dirac delta function
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.
scientific article; zbMATH DE number 4131578