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

Here are various nodal distributions that illustrate the underlying tensor product structures across three quadrants. To implement this effectively, your one-dimensional operator must be one order higher than the desired final multidimensional operator, specifically D minus one orders higher.

In the results presented, we compare 2D representations on the left with 3D representations on the right. The notation used includes TPSS, which stands for Tensor Product Split Simplex, and SVP, which refers to the Split Boundary Operator.

The open symbols represent the multidimensional operator, while the solid symbols denote the new operators. By matching colors, you can observe a significant advantage in freedom and solution error.

This example focuses on an isotropic vortex problem. Notably, we applied extensive warping and skewing to the meshes. Interestingly, despite these distortions, we are not encountering the expected issues typically associated with highly distorted meshes. Additionally, we present normalized comparisons of residual computation times.