Monday, February 19, 2018 - 14:00 in V5-148
Nonnegativity preserving convergent schemes for stochastic porous-medium equations
A talk in the Other series by
Hubertus Grillmeier from University of Erlangen-Nuremberg
| Abstract: |
Having the property of finite speed of propagation, stochastic porous-medium equations constitute free boundary problems.
In this talk, we give some first quantitative results how noise influences the motion of the free boundary.
To this purpose, we propose a fully discrete finite-element scheme for a stochastic
porous-medium equation with linear multiplicative noise given by a source term.
A subtle discretization of the degenerate diffusion coefficient combined with a noise
approximation by bounded stochastic increments permits us to prove H1-regularity
and nonnegativity of discrete solutions. By Nikolsk’ii estimates in time, Skorokhod-type
arguments and the martingale representation theorem, convergence of appropriate
subsequences towards a weak solution is established.
Finally, we present numerical simulations to investigate quantitatively the impact
of noise on occurrence and size of waiting times.
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