Yueyuan Gao

Finite volume methods for deterministic and stochastic PDEs

• Broschiertes Buch

Produktbeschreibung

This thesis bears on numerical methods for deterministic and stochastic partial differential equations; we perform numerical simulations by means of finite volume methods and prove convergence results. In Chapter 1, we apply a semi-implicit time scheme together with the generalized finite volume method SUSHI for the numerical simulation of density driven flows in porous media. In Chapter 2, We perform Monte-Carlo simulations in the one-dimensional torus for the first order Burgers equation forced by a stochastic source term with zero spatial integral. In Chapter 3, we study the convergence of a time explicit finite volume method with an upwind scheme for a first order conservation law with a monotone flux function and a multiplicative source term involving a Q-Wiener process. In Chapter 4, we obtain similar results as in Chapter 3, in the case that the flux function is non-monotone, and that the convection term is discretized by means of a monotone scheme.

Produktdetails

• Verlag: Éditions universitaires européennes
• Seitenzahl: 196
• Erscheinungstermin: 10. Oktober 2016
• Englisch
• Abmessung: 220mm x 150mm x 12mm
• Gewicht: 278g
• ISBN-13: 9783841612380
• ISBN-10: 3841612385
• Artikelnr.: 46900383

Autorenporträt

2012¿2015 Ph.D. student in Mathematics, Advisor: Danielle Hilhorst, Thesis defended on December 10, 2015 at University Paris-Sud, Orsay, France. 2011¿2012 Master of Science, PDE and Scientific computing, University Paris-Sud, Orsay, France. 2007-2011 Bachelor of Science, Mathematics and Applied Mathematics, Wuhan University, P.R. China.