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

Jad Doghman

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arXiv · 2204.13924

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

Jad Doghman

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Abstract

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 $\epsilon$. 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 $\epsilon$ to ensure convergence within the best rate.

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Jad Doghman. 2022-04-29. Numerical approximation of the stochastic Navier-Stokes equations through artificial compressibility. https://arxiv.org/abs/2204.13924

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