2025/12/19 by Niklas Sapountzoglou, Sapountzoglou, Niklas, Aleksandra Zimmermann +1
Decision Sciences · Economics, Econometrics and Finance · Materials Science · #35K55 #60H15 #65M08 #Analysis of PDEs (math.AP) #FOS: Mathematics #Numerical Analysis (math.NA) #Probabilistic and Robust Engineering Design #Probability (math.PR) #Solidification and crystal growth phenomena #Stochastic processes and financial applications
paper · doi:10.48550/arxiv.2512.17712
openalex publication_date 2025/12/19 · openalex created_date 2025/12/23 · openalex updated_date 2026/07/28
This contribution provides numerical experiments for a finite volume scheme for an approximation of the stochastic Allen-Cahn equation with homogeneous Neumann boundary conditions. The approximation is done by a Yosida approximation of the subdifferential operator. The problem is set on a polygonal bounded domain in two or three dimensions. The non-linear character of the projection term induces challenges to implement the scheme. To this end, we provide a splitting method for the finite volume scheme. We show that the splitting method is accurate. The computational error estimates induce that the squared L2-error w.r.t. time is of order 1 as long as the noise term is small enough. For larger noise terms the order of convergence w.r.t. time might become worse.