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We demonstrate how meshfree finite difference methods can be applied to solvevector Poisson problems with electric boundary conditions. In these, thetangential velocity and the incompressibility of the vector field areprescribed at the boundary. Even on irregular domains with only convex corners,canonical nodal-based finite elements may converge to the wrong solution due toa version of the Babuska paradox. In turn, straightforward meshfree finitedifferences converge to the true solution, and even high-order accuracy can beachieved in a simple fashion. The methodology is then extended to a specificpressure Poisson equation reformulation of the Navier-Stokes equations thatpossesses the same type of boundary conditions. The resulting numericalapproach is second order accurate and allows for a simple switching between anexplicit and implicit treatment of the viscosity terms.

Meshfree finite differences for vector Poisson and pressure Poisson equations with electric boundary conditions