2018/05/08 by Michael Multerer, Multerer, M. D.
Computer Science · Decision Sciences · Engineering · #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #FOS: Mathematics #Numerical Analysis (math.NA) #Probabilistic and Robust Engineering Design
paper · pdf · doi:10.48550/arxiv.1805.02889
openalex publication_date 2018/05/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this article, we consider elliptic diffusion problems on random domains with non-smooth diffusion coefficients. We start by illustrating the problems that arise from a non-smooth diffusion coefficient by recapitulating the corresponding regularity analysis. Then, we propose an alternative approach to address this problem by means of a perturbation method. Based on the assumption that the diffusion coefficient can be decomposed in a possibly deterministic, analytic part and a rough random perturbation, we derive approximation results in terms of the perturbations amplitude for the approximation of quantities of interest of the solution. Numerical examples are given in order to validate and quantify the theoretical results.