Open AccessNumerical simulations for the newton and stokes potentials using approximate approximations
Author(s) -
Werner Varnhorn,
Saphir Mfogo
Publication year - 2022
Publication title -
journal of computational mathematics
Language(s) - English
Resource type - Journals
ISSN - 2456-8686
DOI - 10.26524/cm128
Subject(s) - approximations of π , partition (number theory) , smoothness , mathematics , numerical approximation , numerical analysis , stokes flow , stokes problem , poisson distribution , mathematical analysis , physics , geometry , combinatorics , finite element method , flow (mathematics) , statistics , thermodynamics
The method of approximate approximations is based on generating functions representing an approximate partition of the unity. In the present paper this method is used for the numerical solution of the Poisson equation and the Stokes system in Rn (n = 2, 3). The corresponding approximate volume potentials will be computed explicitly in these cases,containing a one-dimensional integral, only. Numerical simulations show the efficiency of the method and confirm the expected approximation of essentially second order, depending on the smoothness of the data.