2022/01/21 by Ľubomír Baňas, Baňas, Ľubomír, Christian Vieth +1 · 1 citation
Computer Science · Materials Science · #Advanced Mathematical Modeling in Engineering #Solidification and crystal growth phenomena
paper · pdf · doi:10.48550/arxiv.2201.08641
We derive a posteriori error estimates for a fully discrete finite element approximation of the stochastic Cahn-Hilliard equation. The a posteriori bound is obtained by a splitting of the equation into a linear stochastic partial differential equation (SPDE) and a nonlinear random partial differential equation (RPDE). 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 stochastic noise. We provide numerical simulations to demonstrate the practicability of the proposed adaptive algorithm.