The spectral element method for the shallow water equations on the sphere
Journal of Computational Physics
Proceedings of the 2003 ACM/IEEE conference on Supercomputing
International Journal of High Performance Computing Applications
The NCAR Spectral Element Climate Dynamical Core: Semi-Implicit Eulerian Formulation
Journal of Scientific Computing
Journal of Computational Physics
CAM-SE: A scalable spectral element dynamical core for the Community Atmosphere Model
International Journal of High Performance Computing Applications
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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 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.