Optimal analysis of finite element methods for the stochastic Stokes equations

06/28/2022
by   Buyang Li, et al.
0

Numerical analysis for the stochastic Stokes/Navier-Stokes equations is still challenging even though it has been well done for the corresponding deterministic equations. In particular, the existing error estimates of finite element methods for the stochastic equations all suffer from the order reduction with respect to the spatial discretizations. The best convergence result obtained for these fully discrete schemes is only half-order in time and first-order in space, which is not optimal in space in the traditional sense. The purpose of this article is to establish the strong convergence of O(τ^1/2+ h^2) and O(τ^1/2+ h) in the L^2 norm for the inf-sup stable velocity-pressure finite element approximations, where τ and h denote the temporal stepsize and spatial mesh size, respectively. The error estimates are of optimal order for the spatial discretization considered in this article (with MINI element), and consistent with the numerical experiments. The analysis is based on the fully discrete Stokes semigroup technique and the corresponding new estimates.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
02/08/2022

Optimal L^2 error estimates of the penalty finite element method for the unsteady Navier-Stokes equations with nonsmooth initial data

In this paper, both semidiscrete and fully discrete finite element metho...
research
03/18/2022

New analysis of Mixed finite element methods for incompressible Magnetohydrodynamics

The paper focuses on a new error analysis of a class of mixed FEMs for s...
research
07/08/2019

A convergent FV-FEM scheme for the stationary compressible Navier-Stokes equations

In this paper, we propose a discretization of the multi-dimensional stat...
research
12/07/2020

Expandable Local and Parallel Two-Grid Finite Element Scheme for the Stokes Equations

In this paper, we present a novel local and parallel two-grid finite ele...
research
04/07/2022

Analysis of a class of globally divergence-free HDG methods for stationary Navier-Stokes equations

This paper analyzes a class of globally divergence-free (and therefore p...

Please sign up or login with your details

Forgot password? Click here to reset