Abstract

The spectral element method is well known as an efficient way to obtain high-order numerical solutions on unstructured finite element grids. However, the oscillatory nature of the method’s advection operator makes it unsuitable for many applications. One popular way to address this problem is wit... Show moreThe spectral element method is well known as an efficient way to obtain high-order numerical solutions on unstructured finite element grids. However, the oscillatory nature of the method’s advection operator makes it unsuitable for many applications. One popular way to address this problem is with high-order discontinuous-Galerkin methods. In this work, an alternative solution which fits within the continuous Galerkin formulation of the spectral element method is proposed. Making use of a compatible formulation of spectral elements, a natural way to implement conservative non-oscillatory reconstructions for spectral element advection is shown. The reconstructions are local to the element and thus preserve the parallel efficiency of the method. Numerical results from a low-order quasi-monotone reconstruction and a higher-order sign-preserving reconstruction are presented. Show less