Robust a posteriori estimates for the stochastic Cahn-Hilliard equation.
A talk in the BI.discrete Workshop series by
L’ubomír Baňas from Bielefeld
| Abstract: | We discuss robust a posteriori error estimates for a fully discrete finite element approximation of the stochastic Cahn-Hilliard equation with additive noise. We derive the a posteriori bound by splitting the equation into a linear stochastic partial differential equation and a nonlinear random partial differential equation and estimate the errors for the respective equations on suitable probability subsets. The resulting estimate is robust with respect to the interfacial width parameter and is computable since it involves the discrete principal eigenvalue of a linearized (stochastic) Cahn-Hilliard operator. Furthermore, the estimate is robust with respect to topological changes as well as the intensity of the noise. We propose an adaptive algorithm based on the derived estimate and present numerical simulations to demonstrate the practicability of the proposed approach. The talk is based on a joint work with Christian Vieth. Within the CRC this talk is associated to the project(s): A7, B3, B7 |