New Higher-Order Mass-Lumped Tetrahedral Elements for Wave Propagation Modelling
Abstract
We present a new accuracy condition for the construction of continuous mass-lumped elements. This condition is less restrictive than the one currently used and enabled us to construct new mass-lumped tetrahedral elements of degrees 2 to 4. The new degree-2 and degree-3 tetrahedral elements require 15 and 32 nodes per element, respectively, while currently, these elements require 23 and 50 nodes, respectively. The new degree-4 elements require 60, 61 or 65 nodes per element. Tetrahedral elements of this degree had not been found yet. We prove that our accuracy condition results in a mass-lumped finite element method that converges with optimal order in the -norm and energy-norm. A dispersion analysis and several numerical tests confirm that our elements maintain the optimal order of accuracy and show that the new mass-lumped tetrahedral elements are more efficient than the current ones.
Cite
@article{arxiv.1803.10065,
title = {New Higher-Order Mass-Lumped Tetrahedral Elements for Wave Propagation Modelling},
author = {S. Geevers and W. A. Mulder and J. J. W. van der Vegt},
journal= {arXiv preprint arXiv:1803.10065},
year = {2019}
}