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On the boundary element method for Stokes flow in domains with discontinuous boundaries
Author(s) -
Rajski Michal P.,
Harmel Maximilian,
Sauer Roger A.
Publication year - 2021
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.202000309
Subject(s) - classification of discontinuities , boundary element method , boundary (topology) , domain (mathematical analysis) , flow (mathematics) , boundary knot method , constant (computer programming) , element (criminal law) , mathematical analysis , stokes flow , method of fundamental solutions , boundary value problem , mathematics , outflow , rest (music) , geometry , finite element method , computer science , physics , acoustics , political science , meteorology , law , thermodynamics , programming language
The classical boundary element method (BEM) has difficulties capturing the solution accurately in the presence of boundary discontinuities. It exhibits higher error values in the proximity of corners than on the rest of the boundary. In an attempt to remedy this problem a two‐dimensional constant uniform flow across a square domain with an outflow condition on one side is considered and analyzed in depth. This leads to the conclusion that the free term from classical approaches needs to be reformulated for the degrees of freedoms lying at the corner points. This modification improves the accuracy of the BEM up to machine precision, which opens interesting directions for further research.