Ben Moussa, B.; Vila, J. P. Convergence of SPH method for scalar nonlinear conservation laws. (English) Zbl 0949.65095 SIAM J. Numer. Anal. 37, No. 3, 863-887 (2000). The paper is devoted to the study of the convergence of weighted particle approximations by the smooth particle hydrodynamics (SPH) method applied to nonlinear multidimensional conservation laws. The mathematical analysis is performed by connecting this new approach with the finite volume scheme. Convergence of the approximate solution in \(L^p_{\text{loc}}\) \((p<\infty)\) towards the unique weak entropy solution of the Cauchy problem is obtained in the scalar nonlinear case by using uniqueness of measure valued solutions. Reviewer: Laura-Iulia Aniţa (Iaşi) Cited in 1 ReviewCited in 23 Documents MSC: 65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs 35L65 Hyperbolic conservation laws 65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs 76M28 Particle methods and lattice-gas methods 76M12 Finite volume methods applied to problems in fluid mechanics Keywords:weighted particle approximation; conservation laws; convergence; measure valued solutions; smooth particle hydrodynamics method; finite volume scheme; weak entropy solution; Cauchy problem PDFBibTeX XMLCite \textit{B. Ben Moussa} and \textit{J. P. Vila}, SIAM J. Numer. Anal. 37, No. 3, 863--887 (2000; Zbl 0949.65095) Full Text: DOI