A radial basis function WENO method with stencil adaptivity

Abstract

In this paper, the flexibility in the choice of stencil sizes in the radial basis function Weighted Essentially Non-Oscillatory (WENO) reconstruction is used to develop a stencil adaptivity strategy that will be coupled with the WENO method. The size of the stencil is determined by the value of an a posteriori error indicator which determines whether the stencil lies in a smooth region of the solution or across a discontinuity. Numerical results are presented for thin plate spline reconstruction to illustrate the benefits of the proposed method.