High‐order finite elements compared to low‐order mixed element formulations

Abstract

AbstractHigh‐order finite elements are commonly compared with linear element formulations showing that, in terms of the relation between computational time and achievable accuracy, linear element formulations are inferior to high‐order elements. On the other hand, the finite element community follows the h‐version approach due to its simplicity in implementation. This article compares high‐order finite elements based on hierarchic shape functions with low‐order mixed element formulations using finite strain hyperelasticity. These comparisons are conducted from the point of view of both accuracy and efficiency as well as highly deformed structures. It also investigates improvements to minimize the overall computational effort such as parallelizing the element assemblage procedure, choosing a starting vector estimator for Newton's method, and investigating the Newton‐Chord method. The advantages and disadvantages of both finite element approaches are also discussed.