×

Convergence of a semi-discrete kinetic scheme for the system of isentropic gas dynamics with \(\gamma=3\). (English) Zbl 1020.65054

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.

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
Full Text: DOI Link