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

The concept of collapsed coordinates involves transforming a quadrilateral into a triangle by repositioning a vertex. For a hexagon to be converted into a tetrahedron, the process is more complex and requires multiple transformations. This results in a singularity at one vertex in the triangular case, which is why we typically avoid placing a volume quadrature node at that location.

By utilizing this approach, we can apply the same tensor product algorithm, which reduces the number of flux evaluations needed on the simplex. I will provide a high-level overview today, and at the conclusion of my presentation, I will reference relevant papers for those seeking more detailed information.