Nested finite element approximation of parabolic SPDEs with Whittle-Mat\'ern noise

Autor:	Auestad, Øyvind Stormark
Rok vydání:	2024
Předmět:	Mathematics - Numerical Analysis 65C30 65C20 35K10 35K51 60H15
Druh dokumentu:	Working Paper
Popis:	We propose a new type of fully discrete finite element approximation of a class of semilinear stochastic parabolic equations with additive noise. Our discretization differs from the ones typically considered, in that we employ a nested finite element approximation of the noise. This is well suited for dealing with covariance operators defined in terms of (negative powers of) elliptic operators, like that of Whittle-Mat\'ern random fields. We derive strong and pathwise convergence rates for our proposed discretization, and our results are supported by numerical experiments. Comment: Disclaimer: this is a preliminary version of joint work between {\O}yvind Stormark Auestad, Annika Lang, Espen Jakobsen and Geir-Arne Fuglstad. A final version with this list of authors will be uploaded later
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2406.11041 Zobrazit plný text záznamu View this record from Arxiv