High order transition elements: The xNy-element concept, Part II: Dynamics

In this article, the construction of versatile transition elements for applications in dynamics is comprehensively discussed. Based on the transfinite mapping technique, also known as Coons-Gordon interpolation, piece-wise shape functions are derived such that an arbitrary number of elements with different ansatz spaces is coupled conformingly. This is an important prerequisite to enable the use of local mesh refinement strategies for regular quadrilateral discretizations. Due to the special construction of the shape functions, there are no hanging nodes that need to be taken care of. The focus in this contribution is on dynamics, and therefore, Lagrange polynomials are taken as the basis to construct shape functions for arbitrary transition elements. As a consequence, the Kronecker-delta and partition of unity properties are recovered. These properties are crucial to diagonalize the mass matrix using standard mass lumping techniques such as row-summing and diagonal scaling. The performance of the proposed family of elements is assessed by means of several benchmark examples, where the numerical rates of convergence are determined for both consistent and lumped mass matrix formulations. (C) 2021 Elsevier B.V. All rights reserved.

Automated summary

This article comprehensively discusses the construction and performance assessment of versatile transition elements for applications in dynamics, focusing on the use of special shape function construction to achieve diagonalization of the mass matrix.