Hyperviscosity

One of the most common drawbacks of the RBF-FD method is its stability. Furthermore, the RBF-FD method, due to scattered nodes, sometimes produces system (differential) matrices with spurious eigenvalues. Those are far more common than with for example FVM or FEM method.

For such unstable systems, one usually considers numerical diffusion in the form of hyperviscosity. The hyperviscosity scheme introduces higher-order Laplacian operator (i.e. hyperviscosity operator) to the right hand side of the PDE

$$ +\gamma \Delta^\alpha u, $$

where $\gamma$ is a hyperviscosity constant and $\alpha$ is the order of hyperviscosity.