A Comparison of Methods for Gradient Field Estimation on Simplicial Meshes

The estimation of the differential properties of a function sampled at the vertices of a discrete domain is at the basis of many applied sciences. In this paper, we focus on the computation of function gradi- ents on triangle and tetrahedral meshes. We study one cell-based method (the standard the facto), plus three vertex-based methods. Comparisons regard accuracy, ability to perform on different domain dis- cretizations, and efficiency. We performed extensive tests and provide an in-depth analysis of our results. Besides some common behaviour, we found that some methods perform better than others, consider- ing both accuracy and efficiency. This directly translates to useful suggestions for the implementation of gradient estimators in research and industrial code.