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A numerical scheme for approximating interior jump discontinuity solution of a compressible Stokes system

Title
A numerical scheme for approximating interior jump discontinuity solution of a compressible Stokes system
Authors
KWEON, JAE RYONGHan, Joo-Hyeong
POSTECH Authors
KWEON, JAE RYONG
Date Issued
Jan-2019
Publisher
Elsevier
Abstract
In this paper we develop a numerical scheme for approximating interior jump discontinuity solutions of compressible Stokes flows with inflow jump datum. The scheme is based on a decomposition of the velocity vector into three parts: the jump part, an auxiliary one and the smoother one. The jump discontinuity is handled by constructing a vector function extending the density jump value of the normal vector on the interface to the whole domain. We show existence of the finite element solutions for the three parts, derive error estimates and also convergence rates based on the piecewise regularities. Numerical examples are given, confirming the derived convergence rates.
In this paper we develop a numerical scheme for approximating interior jump discontinuity solutions of compressible Stokes flows with inflow jump datum. The scheme is based on a decomposition of the velocity vector into three parts: the jump part, an auxiliary one and the smoother one. The jump discontinuity is handled by constructing a vector function extending the density jump value of the normal vector on the interface to the whole domain. We show existence of the finite element solutions for the three parts, derive error estimates and also convergence rates based on the piecewise regularities. Numerical examples are given, confirming the derived convergence rates.
Keywords
Computational methods; Convergence rates; Error estimates; Finite element solution; Jump discontinuities; Numerical scheme; Regularity; Vector functions; Velocity vectors; Mathematical techniques
URI
http://oasis.postech.ac.kr/handle/2014.oak/94115
DOI
10.1016/j.cam.2018.06.039
ISSN
0377-0427
Article Type
Article
Citation
J. Comput. Appl. Math., vol. 345, no. 1, page. 320 - 337, 2019-01
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 KWEON, JAE RYONG
Dept of Mathematics
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