Non-smooth kernels for meshfree methods in fluid dynamics
A function and its first two derivatives are estimated by convolutions with well-chosen non-differentiable kernels. The convolutions are in turn approximated by NewtonCotes integration techniques with the aid of a polynomial interpolation based on an arbitrary finite set of points. Precise numerical results are obtained with far fewer points than that in classic SPH, and error bounds are derived.
non-smooth kernels meshfree methods error bounds sph method