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Ouvrages Année : 2022

A two-step numerical scheme in time for surface quasi geostrophic equations under location uncertainty

Résumé

In this work we consider the surface quasi-geostrophic (SQG) system under location uncertainty (LU) and propose a Milstein-type scheme for these equations, which is then used in a multi-step method. The SQG system considered here consists of one stochastic partial differential equation, which models the stochastic transport of the buoyancy, and a linear operator linking the velocity and the buoyancy. In the LU setting, the Euler-Maruyama scheme converges with weak order 1 and strong order 0.5. Our aim is to develop higher order schemes in time, based on a Milstein-type scheme in a multi-step framework. First we compared different kinds of Milstein schemes. The scheme with the best performance is then included in the two-step scheme. Finally, we show how our two-step scheme decreases the error in comparison to other multi-step schemes.
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Dates et versions

hal-03695944 , version 1 (15-06-2022)

Identifiants

  • HAL Id : hal-03695944 , version 1

Citer

Camilla Fiorini, Pierre-Marie Boulvard, Long Li, Étienne Mémin (Dir.). A two-step numerical scheme in time for surface quasi geostrophic equations under location uncertainty. pp.1-10, inPress. ⟨hal-03695944⟩
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