Nonlinearly-Stable High-Order Methods on Simplices with Improved Efficiency

In our analysis, we observe consistent trends. For instance, in the best-case scenario where 3D p equals 5, we can utilize the Tensor-Product Split-Simplex operator alongside the Multidimensional SVP. By comparing the same workload, we can assess the reduction in error, which is approximately a quarter. Alternatively, if we focus on achieving a specific error, we can save time by a factor of 20.

The results vary depending on the order and the specific methods employed. We have identified two effective approaches for implementing high-order schemes on simplices that are entropy stable and may offer competitive advantages.

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