In a surprising upset, quadratic tetrahedral elements performed similarly or better than hexahedral elements for a range of elliptic PDEs, particularly when considering the entire FEM pipeline from meshing to solving. This suggests that robust, automatic tetrahedral meshing, coupled with quadratic elements, can be a strong choice for many common simulation scenarios without sacrificing performance.

The authors received gifts from Adobe Research, nTopology, and Advanced Micro Devices, Inc. However, the study focuses on a general comparison of element types and utilizes open-source software and publicly available datasets, reducing potential bias. No direct conflict related to the specific findings is apparent.

This study provides a valuable large-scale comparison of tetrahedral and hexahedral elements for common elliptic PDEs, using real-world geometries and state-of-the-art meshing tools. The benchmark and code release are significant contributions to the FEM community. While limited to specific scenarios and solvers, the methodology is sound, the findings relevant, and the scope extensive enough to warrant a strong rating. The identified limitations, particularly regarding solver influence, and meshing robustness, don't invalidate the findings but suggest further research directions. No obvious bias due to declared gifts is identified.