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Pré-Publication, Document De Travail Année : 2023

Numerical approximation of the stochastic Navier-Stokes equations through artificial compressibility

Jad Doghman
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Résumé

A constructive numerical approximation of the two-dimensional unsteady stochastic Navier-Stokes equations of an incompressible fluid is proposed via a pseudo-compressibility technique involving a parameter ε. Space and time are discretized through a finite element approximation and an Euler method. The convergence analysis of the suggested numerical scheme is investigated throughout this paper. It is based on a local monotonicity property permitting the convergence toward the unique strong solution of the Navier-Stokes equations to occur within the originally introduced probability space. Justified optimal conditions are imposed on the parameter ε to ensure convergence within the best rate.
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Dates et versions

hal-03653870 , version 1 (28-04-2022)
hal-03653870 , version 2 (12-04-2023)

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Jad Doghman. Numerical approximation of the stochastic Navier-Stokes equations through artificial compressibility: Numerical analysis of the stochastic Navier-Stokes. 2023. ⟨hal-03653870v2⟩
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