Finite volume methods for deterministic and stochastic PDEs

Finite volume methods for deterministic and stochastic PDEs
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ISBN: 9783841612380
Autor: Yueyuan Gao
Einband/Bindung: Taschenbuch
Sprache: Englisch
Seitenzahl: 196
Erscheinungsjahr: 2016
Verlag: Editions Universitaires Europeennes EUE
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Beschreibung
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.
Artikel-Nr.: 9783841612380
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