“…In this article, a p-version finite element formulation based on hierarchic shape functions whose bases are integrated Legendre-polynomials, see [49] and [13], is not only compared with linear and quadratic hexahedral or tetrahedral elements but also with mixed hexahedral elements such as Q1P0-and Q2P1-elements proposed by [45] or [46]. Moreover, some improvements have been selected to accelerate the computation, such as estimating the starting vector of the Newton method: see, for example, [23], to apply the Newton-Chord method: see [28] or, in the context of finite elements, the modified Newton method, see [1]. This has a particularly beneficial effect on the p-version FEM with regard to the computational effort required to assemble element matrices.…”