Vasseur, Alexis Convergence of a semi-discrete kinetic scheme for the system of isentropic gas dynamics with \(\gamma=3\). (English) Zbl 1020.65054 Indiana Univ. Math. J. 48, No. 1, 347-364 (1999). Summary: We consider, for the system of isentropic gas dynamics with \(\gamma+3\), a time-discrete kinetic scheme, closely related to the kinetic formulation of Lions, Perthame, and Tadmor. We prove the convergence of this scheme by using averaging lemmas and we show that the convergence is strong in \(L^1_{\text{loc}}\), even at the microscopic level. Cited in 9 Documents MSC: 65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs 76M25 Other numerical methods (fluid mechanics) (MSC2010) 35L65 Hyperbolic conservation laws 76N15 Gas dynamics (general theory) Keywords:averaging PDFBibTeX XMLCite \textit{A. Vasseur}, Indiana Univ. Math. J. 48, No. 1, 347--364 (1999; Zbl 1020.65054) Full Text: DOI Link