Extraction method for Stokes Flow with jumps in the pressure
It provides a practical method for solving Stokes flow with interface singularities, which is relevant for computational fluid dynamics problems involving immersed boundaries or multiphase flows.
The paper develops a new numerical scheme for stationary Stokes flow with pressure jumps along interfaces, enabling the use of uniform grids and achieving optimal convergence rates (O(h) for pressure, O(h^2) for velocity).
In this paper, we consider a stationary, constant viscosity, incompressible Stokes flow with singular forces along one or several interfaces. Assuming only the jumps of the pressure are present along the interface, we develop a new numerical scheme for such a problem. By constructing an approximate singular function and removing it, we can apply a standard finite element method to solve it. A main advantage of our scheme is that one can use a uniform grid. We observe optimal $O(h)$ order for the pressure and $O(h^2)$ order for the velocity.