Efficient Computation of the Minimum of Shape Quality Measures on Curvilinear Finite Elements

We present a method for computing robust shape quality measures defined for any order of finite elements. All type of elements are considered, including pyramids. The measures are defined as the minimum of the pointwise quality of curved elements. The computation of the minimum, based on previous work presented by Johnen et al. (2013) [1,2], is very efficient. The key feature is to expand polynomial quantities into Bézier bases which allows to compute sharp bounds on the minimum of the pointwise quality measures.