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

The following slide presents various nodal distributions that illustrate the underlying tensor product structures in three quadrilaterals. To achieve successful implementation, the one-dimensional operator must be one order higher than the desired output, specifically D minus one orders higher for the final multidimensional operator.

The results shown compare two-dimensional data on the left with three-dimensional data on the right. The notation used includes TPSS, which stands for Tensor Product Split Simplex, and SVP, which refers to a specific type of spatial variation principle.