2023/04/05 by Caroline Bauzet, Bauzet, Caroline, Kerstin Schmitz +3 · 2 citations
Economics, Econometrics and Finance · #35K05 #60H15 #65M08 #Analysis of PDEs (math.AP) #FOS: Mathematics #Numerical Analysis (math.NA) #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.2304.02259
openalex publication_date 2023/04/05 · openalex created_date 2023/04/27 · openalex updated_date 2026/07/28
We address an original approach for the convergence analysis of a finite-volume scheme for the approximation of a stochastic diffusion-convection equation with multiplicative noise in a bounded domain of ℝd (with d=2 or 3) and with homogeneous Neumann boundary conditions. The idea behind our approach is to avoid using the stochastic compactness method. We study a numerical scheme that is semi-implicit in time and in which the convection and the diffusion terms are respectively approximated by means of an upwind scheme and the so called two-point flux approximation scheme (TPFA). By adapting well-known methods for the time discretization of stochastic PDEs and combining them with deterministic techniques applied to spatial discretization, we show strong convergence of our scheme towards the unique variational solution of the continuous problem in Lp(0,T;L2(Ω;L2(Λ))), for any finite p≥ 1.