A comparison of methods for gradient field estimation on simplicial meshes

Abstract 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 gradients 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 discretizations, 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, considering both accuracy and efficiency. This directly translates to useful suggestions for the implementation of gradient estimators in research and industrial code.