Influence of Gauss and Gauss‐Lobatto quadrature rules on the accuracy of a quadrilateral finite element method in the time domain

Abstract

Abstract In this article, we examine the influence of numerical integration on finite element methods using quadrilateral or hexahedral meshes in the time domain. We pay special attention to the use of Gauss‐Lobatto points to perform mass lumping for any element order. We provide some theoretical results through several error estimates that are completed by various numerical experiments. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2009