Higher Order Finite Element Methods

Abstract

The efficiency of numerical methods for wave propagation analysis is essential, as very fine spatial and temporal resolutions are required in order to properly describe all the phenomena of interest, such as scattering, reflection, mode conversion, and many more. These strict demands originate from the fact that high-frequency ultrasonic guided waves are investigated. In the current chapter, we focus on the finite element method (FEM) based on higher order basis functions and demonstrate its range of applicability. Thereby, we discuss the p-FEM, the spectral element method (SEM), and the isogeometric analysis (IGA). Additionally, convergence studies demonstrate the performance of the different higher order approaches with respect to wave propagation problems. The results illustrate that higher order methods are an effective numerical tool to decrease the numerical costs and to increase the accuracy. Furthermore, we can conclude that FE-based methods are principally able to tackle all wave propagation-related problems, but they are not necessarily the most efficient choice in all situations.