2023/06/22 by Jérôme Droniou, Droniou, Jerome, Muhammad Awais Khan +3 · 1 citation
Computer Science · Engineering · Materials Science · #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Magnetic Properties and Applications #Numerical Analysis (math.NA) #Topology Optimization in Engineering
paper · pdf · doi:10.48550/arxiv.2306.12668
openalex publication_date 2023/06/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The gradient discretisation method (GDM) -- a generic framework encompassing many numerical methods -- is studied for a general stochastic Stefan problem with multiplicative noise. The convergence of the numerical solutions is proved by compactness method using discrete functional analysis tools, Skorohod theorem and the martingale representation theorem. The generic convergence results established in the GDM framework are applicable to a range of different numerical methods, including for example mass-lumped finite elements, but also some finite volume methods, mimetic methods, lowest-order virtual element methods, etc. Theoretical results are complemented by numerical tests based on two methods that fit in GDM framework.