Paper Info
Title
Rates of Convergence for Discretizations of the Stochastic Incompressible Navier-Stokes Equations.
Abstract
We show strong convergence with rates for an implicit time discretization, a semi-implicit time discretization, and a related finite element based space-time discretization of the incompressible Navier-Stokes equations with multiplicative noise in two space dimensions. We use higher moments of computed iterates to optimally bound the error on a subset Omega(kappa). of the sample space Omega, where corresponding paths are bounded in a proper function space, and P[Omega(kappa)] -> 1 holds for vanishing discretization parameters. This implies convergence in probability with rates, and motivates a practicable acception/rejection criterion to overcome possible pathwise explosion behavior caused by the nonlinearity. It turns out that it is the interaction of Lagrange multipliers with the stochastic forcing in the scheme which limits the accuracy of general discretely LBB-stable space discretizations, and strategies to overcome this problem are proposed.
Year
DOI
Venue
2012
10.1137/110845008
SIAM JOURNAL ON NUMERICAL ANALYSIS
Keywords
Field
DocType
stochastic Navier-Stokes equation,space-time discretization,strong convergence with rates
Convergence of random variables,Discretization,Function space,Mathematical optimization,Mathematical analysis,Lagrange multiplier,Finite element method,Sample space,Mathematics,Bounded function,Navier–Stokes equations
Journal
Volume
Issue
ISSN
50
5
0036-1429
Citations 
PageRank 
References 
5
0.92
0
Authors
2
Name
Order
Citations
PageRank
Erich Carelli192.13
Andreas Prohl230267.29