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.
|Number of pages||1|
|Publication status||Published - 2019|
|Event||90th Annual Meeting of the International Association of Applied Mathematics and Mechanics - Vienna University of Technology, Vienna, Austria|
Duration: 18 Feb 2019 → 22 Feb 2019
|Conference||90th Annual Meeting of the International Association of Applied Mathematics and Mechanics|
|Period||18/02/19 → 22/02/19|