Convergence of a finite-volume scheme for a heat equation with a multiplicative stochastic force

Caroline Bauzet; Flore Nabet

doi:10.1007/978-3-030-43651-3_24

Convergence of a finite-volume scheme for a heat equation with a multiplicative stochastic force

Caroline Bauzet
, Flore Nabet

Centre national de la recherche scientifique

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

We present here the discretization by a finite-volume scheme of a heat equation perturbed by a multiplicative noise of Itô type and under homogeneous Neumann boundary conditions. The idea is to adapt well-known methods in the deterministic case for the approximation of parabolic problems to our stochastic PDE. In this paper, we try to highlight difficulties brought by the stochastic perturbation in the adaptation of these deterministic tools.

Original language	English
Title of host publication	Finite Volumes for Complex Applications IX - Methods, Theoretical Aspects, Examples, FVCA 2020
Editors	Robert Klöfkorn, Eirik Keilegavlen, Florin A. Radu, Jürgen Fuhrmann
Publisher	Springer
Pages	275-283
Number of pages	9
ISBN (Print)	9783030436506
DOIs	https://doi.org/10.1007/978-3-030-43651-3_24
Publication status	Published - 1 Jan 2020
Event	9th International Symposium on Finite Volumes for Complex Applications, FVCA 2020 - Bergen, Norway Duration: 15 Jun 2020 → 19 Jun 2020

Publication series

Name	Springer Proceedings in Mathematics and Statistics
Volume	323
ISSN (Print)	2194-1009
ISSN (Electronic)	2194-1017

Conference

Conference	9th International Symposium on Finite Volumes for Complex Applications, FVCA 2020
Country/Territory	Norway
City	Bergen
Period	15/06/20 → 19/06/20

Keywords

Finite volume method
Itô formula
Itô integral
Multiplicative noise
Predictable process
Stochastic heat equation

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10.1007/978-3-030-43651-3_24

Cite this

Bauzet, C., & Nabet, F. (2020). Convergence of a finite-volume scheme for a heat equation with a multiplicative stochastic force. In R. Klöfkorn, E. Keilegavlen, F. A. Radu, & J. Fuhrmann (Eds.), Finite Volumes for Complex Applications IX - Methods, Theoretical Aspects, Examples, FVCA 2020 (pp. 275-283). (Springer Proceedings in Mathematics and Statistics; Vol. 323). Springer. https://doi.org/10.1007/978-3-030-43651-3_24

Bauzet, Caroline ; Nabet, Flore. / Convergence of a finite-volume scheme for a heat equation with a multiplicative stochastic force. Finite Volumes for Complex Applications IX - Methods, Theoretical Aspects, Examples, FVCA 2020. editor / Robert Klöfkorn ; Eirik Keilegavlen ; Florin A. Radu ; Jürgen Fuhrmann. Springer, 2020. pp. 275-283 (Springer Proceedings in Mathematics and Statistics).

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abstract = "We present here the discretization by a finite-volume scheme of a heat equation perturbed by a multiplicative noise of It{\^o} type and under homogeneous Neumann boundary conditions. The idea is to adapt well-known methods in the deterministic case for the approximation of parabolic problems to our stochastic PDE. In this paper, we try to highlight difficulties brought by the stochastic perturbation in the adaptation of these deterministic tools.",

keywords = "Finite volume method, It{\^o} formula, It{\^o} integral, Multiplicative noise, Predictable process, Stochastic heat equation",

author = "Caroline Bauzet and Flore Nabet",

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Bauzet, C & Nabet, F 2020, Convergence of a finite-volume scheme for a heat equation with a multiplicative stochastic force. in R Klöfkorn, E Keilegavlen, FA Radu & J Fuhrmann (eds), Finite Volumes for Complex Applications IX - Methods, Theoretical Aspects, Examples, FVCA 2020. Springer Proceedings in Mathematics and Statistics, vol. 323, Springer, pp. 275-283, 9th International Symposium on Finite Volumes for Complex Applications, FVCA 2020, Bergen, Norway, 15/06/20. https://doi.org/10.1007/978-3-030-43651-3_24

Convergence of a finite-volume scheme for a heat equation with a multiplicative stochastic force. / Bauzet, Caroline; Nabet, Flore.
Finite Volumes for Complex Applications IX - Methods, Theoretical Aspects, Examples, FVCA 2020. ed. / Robert Klöfkorn; Eirik Keilegavlen; Florin A. Radu; Jürgen Fuhrmann. Springer, 2020. p. 275-283 (Springer Proceedings in Mathematics and Statistics; Vol. 323).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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N1 - Publisher Copyright: © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2020.

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AB - We present here the discretization by a finite-volume scheme of a heat equation perturbed by a multiplicative noise of Itô type and under homogeneous Neumann boundary conditions. The idea is to adapt well-known methods in the deterministic case for the approximation of parabolic problems to our stochastic PDE. In this paper, we try to highlight difficulties brought by the stochastic perturbation in the adaptation of these deterministic tools.

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KW - Itô formula

KW - Itô integral

KW - Multiplicative noise

KW - Predictable process

KW - Stochastic heat equation

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DO - 10.1007/978-3-030-43651-3_24

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A2 - Radu, Florin A.

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Y2 - 15 June 2020 through 19 June 2020

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Bauzet C, Nabet F. Convergence of a finite-volume scheme for a heat equation with a multiplicative stochastic force. In Klöfkorn R, Keilegavlen E, Radu FA, Fuhrmann J, editors, Finite Volumes for Complex Applications IX - Methods, Theoretical Aspects, Examples, FVCA 2020. Springer. 2020. p. 275-283. (Springer Proceedings in Mathematics and Statistics). doi: 10.1007/978-3-030-43651-3_24

Convergence of a finite-volume scheme for a heat equation with a multiplicative stochastic force

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