Improved Interpolants for Discontinuous Pressures

Abstract

We consider 2D incompressible Stokes flow with an internal interface at which the pressure is discontinuous, as happens for example in problems involving surface tension. We assume that the internal interface is a line that does not coincide with the mesh edges, and propose a piecewise-linear pressure space with improved interpolation properties. The functions in the proposed space are discontinuous only at the interface, coinciding with standard P functions away from it. Further, the degrees of freedom are exactly the same as those of the standard, conforming P1 space, making it straightforward to incorporate the proposed method in existing codes. We implement the well-known mini-element and show that switching to the proposed pressure space at the elements cut by the interface significantly reduces the error in both pressure and velocity.