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

The slide presents the number of floating point operations involved in local operator evaluation, highlighting similar trends as observed previously. While actual CPU time would provide more insight, the complexities of coding necessitate the use of these metrics instead.

At lower degrees, the benefits are minimal; however, a significant advantage is evident at higher degrees, particularly in three-dimensional or tetrahedral contexts. Additionally, it is important to note that the curve for the tensor product approach extends further than the multidimensional scheme. This is due to the finite number of quadrature rules applicable to multiple dimensions on simplices, in contrast to one-dimensional scenarios where the degree can increase indefinitely. By leveraging the tensor product, we can utilize one-dimensional quadrature rules, allowing for much higher degrees of accuracy.