We present a new accuracy condition for constructing mass-lumped finite elements. This new condition is less restrictive than the one that has been used for several decades and enabled us to construct new mass-lumped tetrahedral elements of degrees 2,3, and 4. The new degree-2 and degree-3 elements require 14 and 32 nodes, respectively, while the degree-2 and degree-3 elements currently available in the literature require 23 and 50 nodes, respectively. Mass-lumped tetrahedral elements of degree 4 had not been found until now. The resulting mass-lumped finite element method is suitable for 3D wave propagation problems, since it can accurately capture the effects of a complex geometry and since it results in a fully explicit time-stepping scheme. A dispersion analysis and several numerical tests illustrates the efficiency of this new method. In particular, they illustrate a significant reduction in degrees of freedom, number of time steps, and computation time for a given accuracy compared to other finite element methods, such as the previous mass-lumped finite element methods or the discontinuous Galerkin method.
Original languageEnglish
Pages362-362
Number of pages1
Publication statusPublished - 2019
Event90th Annual Meeting of the International Association of Applied Mathematics and Mechanics - Vienna University of Technology, Vienna, Austria
Duration: 18 Feb 201922 Feb 2019
https://jahrestagung.gamm-ev.de/index.php/2019/2019-annual-meeting

Conference

Conference90th Annual Meeting of the International Association of Applied Mathematics and Mechanics
Abbreviated titleGAMM2019
CountryAustria
CityVienna
Period18/02/1922/02/19
Internet address

ID: 52735007