Publications de l'Institut Mathématique, Nouvelle Série Vol. 91(105), pp. 137–153 (2012) 

STABILITY AND CONVERGENCE OF THE DIFFERENCE SCHEMES FOR EQUATIONS OF ISENTROPIC GAS DYNAMICS IN LAGRANGIAN COORDINATESPiotr Matus, Dmitry PolyakovInstitute of Mathematics, NAS of Belarus, 11 Surganov Str., 220072 Minsk, Belarus; The John Paul II Catholic University of Lublin, Al. Raclawickie 14, 20950 Lublin, Poland Belarusian State University, Nezavisimosti ave. 4, 220072 Minsk, BelarusAbstract: For the the initialboundary value problem (IBVP) for the isentropic gas dynamics written in Lagrangian coordinates in Riemann invariants we show how the necessary conditions for existence of global smooth solution can be obtained using technics due to P. Lax. Under these conditions we formulate the existence result in the class of piecewisesmooth functions. A priori estimates with respect to the input data for the difference scheme approximating this problem are obtained. Stability estimates are proved using only limitations for the initial and boundary conditions corresponding the differential problem. Estimates of stability in the general case have been obtained only for the finite instant of time $t<t_0$. The monotonicity is proved in both cases. The uniqueness and convergence of the difference solution are also considered. The results of the numerical experiment illustrating theoretical results are given. Keywords: Isentropic gas dynamics; Riemann invariants; Lagrangian coordinates; initialboundary value problem; wellposedness and blowup; finite difference scheme; stability Classification (MSC2000): 65N06; 65M12 Full text of the article: (for faster download, first choose a mirror)
Electronic fulltext finalized on: 10 May 2012. This page was last modified: 12 Jun 2012.
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