| Abstract: |
| The numerical schemes for the approximation of stochastic partial differential equations relies on classical schemes for stochastic differential equations with all the theory concerning strong and weak orders of convergence in time. In this talk the spatial discretization will not be considered, but I will present the proof for the time discretization on the example of phase transitions and fluids dynamics of Allen-Cahn type.
Usually proving the existence of solution and orders of convergence depends on the global Lipschitz regularity of nonlinear terms. But when the nonlinear terms have dissipative effects, it is again possible to define a solution. Actually we can use this type of proof to study the orders of convergence of time schemes, as soon as we can explicitly treat the nonlinear term, for instance via splitting strategies.
In this talk, I will explain how we can prove the weak and strong orders of convergence for approximations of Allen-Cahn equation using splitting strategies, thanks to an explicit treatment of the nonlinear terms. All these results will be validated by numerical experiments. |
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