87 research outputs found
On stochastic conservation laws and Malliavin calculus
For stochastic conservation laws driven by a semilinear noise term, we
propose a generalization of the Kru\v{z}kov entropy condition by allowing the
Kru\v{z}kov constants to be Malliavin differentiable random variables.
Existence and uniqueness results are provided. Our approach sheds some new
light on the stochastic entropy conditions put forth by Feng and Nualart [J.
Funct. Anal., 2008] and Bauzet, Vallet, and Wittbold [J. Hyperbolic Differ.
Equ., 2012]
On the convergence rate of finite difference methods for degenerate convection-diffusion equations in several space dimensions
We analyze upwind difference methods for strongly degenerate
convection-diffusion equations in several spatial dimensions. We prove that the
local -error between the exact and numerical solutions is
, where is the spatial dimension and
is the grid size. The error estimate is robust with respect to
vanishing diffusion effects. The proof makes effective use of specific kinetic
formulations of the difference method and the convection-diffusion equation
- …