Geometrical Validity of High-order Pyramidal Finite Elements

The development of high-order computational methods for solving partial differential equations on unstructured grids has been underway for many years. Such methods critically depend on the availability of high-quality curvilinear meshes, as one badly-shaped element can degrade the solution in the whole domain [2]. The usual way of generating curved meshes is to first generate a straight sided mesh and to curve mesh entities that are classified on the boundaries of the domain. The latter operation introduces a “shape-distortion” that should be controlled if we suppose that the straight sided mesh is composed of well-shaped elements.