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

2022/04/29 by Jad Doghman, Doghman, Jad · 2 citations
Economics, Econometrics and Finance · Decision Sciences · #Stochastic processes and financial applications #Risk and Portfolio Optimization

paper · pdf · doi:10.48550/arxiv.2204.13924

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 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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• Numerical Analysis of 2D Stochastic Navier--Stokes Equations with Transport Noise: Regularity and Spatial Semidiscretization
• An efficient fully explicit scheme for stochastic Navier-Stokes equations driven by multiplicative noise

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