A smooth partition of unity finite element method for vortex particle regularization

We present a new class of C^∞-smooth finite element spaces on Cartesian grids, based on a partition of unity approach. We use these spaces to construct smooth approximations of parti- cle fields, i. e., finite sums of weighted Dirac deltas. In order to use the spaces on general domains, we propose a fictitious domain formulation, together with a new high-order accurate stabilization. Stability, convergence, and conservation properties of the scheme are established. Numerical experi- ments confirm the analysis and show that the Cartesian grid-size _ should be taken proportional to the square-root of the particle spacing h, resulting in significant speed-ups in vortex methods.