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

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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 Itô type and under homogeneous Neumann boundary conditions. The idea is to adapt well-known methods in the de-terministic 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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Dates and versions

hal-02442422 , version 1 (16-01-2020)
hal-02442422 , version 2 (29-01-2020)

Identifiers

  • HAL Id : hal-02442422 , version 2

Cite

Caroline Bauzet, Flore Nabet. Convergence of a finite-volume scheme for a heat equation with a multiplicative stochastic force. Finite Volumes for Complex Applications IX, Jun 2020, Bergen, Norway. ⟨hal-02442422v2⟩
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