Abstract We propose some new mixed finite element methods for the time-dependent stochastic Stokes equations with multiplicative noise, which use Helmholtz decomposition of driving noise. It is known (Langa, J. A., Real, & Simon, (2003) Existence and regularity pressure Navier--Stokes equations. Appl. Math. Optim., 48, 195--210) that solution has low regularity, manifests in suboptimal conv...

A dual formulation and finite element method is proposed and analyzed for simulating the Stefan problem with surface tension. The method uses a mixed form of the heat equation in the solid and liquid (bulk) domains, and imposes a weak formulation of the interface motion law (on the solidliquid interface) as a constraint. The basic unknowns are the heat fluxes and temperatures in the bulk, and t...