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.
| Autorius: | Yueyuan Gao |
| Leidėjas: | Éditions universitaires européennes |
| Išleidimo metai: | 2016 |
| Knygos puslapių skaičius: | 196 |
| ISBN-10: | 3841612385 |
| ISBN-13: | 9783841612380 |
| Formatas: | 220 x 150 x 12 mm. Knyga minkštu viršeliu |
| Kalba: | Anglų |
Parašykite atsiliepimą apie „Finite volume methods for deterministic and stochastic PDEs“
