Hyperviscosity

One of the most commonly mentioned 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. The instabilities arise fastly even with linear PDEs.

With meshless methods (especially RBF-FD) one usually stabilises such schemes by adding a higher-order Laplacian (hyperviscosity) operator on the right-hand side.

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

The final scheme is referred to as hyperviscosity scheme