Analysis and Applied Mathematics Seminar
Liet Vo
UIC
Chorin Projection Methods for Stochastic Stokes Equations
Abstract: In this talk, I will discuss the two fully discrete
Chorin-type projection methods for the stochastic Stokes equations with
general multiplicative noise. The first scheme is the standard Chorin scheme
and the second one is a modified Chorin scheme which is designed by employing the
Helmholtz decomposition on the noise function at each time step to produce
a projected divergence-free noise and a ``pseudo pressure" after combining the original
pressure and the curl-free part of the decomposition.
An $O(k^\frac14)$ rate of convergence is proved for the standard Chorin scheme,
which is sharp but not optimal due to the use of general noise, where $k$ denotes the time mesh size.
On the other hand, an optimal convergence rate $O(k^\frac12)$ is established for the modified Chorin scheme.
The fully discrete finite element methods are formulated by discretizing both semi-discrete Chorin schemes in space by the standard finite element method.
Suboptimal order error estimates are derived for both fully discrete methods. It is proved that
all spatial error constants contain a growth factor $k^{-\frac12}$, where $k$ denotes the
time step size, which explains the deteriorating performance of the standard Chorin scheme
when $k\to 0$.
Monday September 12, 2022 at 4:00 PM in 1227 SEO