Abstract
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 language | English |
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Pages | 362-362 |
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 https://jahrestagung.gamm-ev.de/index.php/2019/2019-annual-meeting |
Conference
Conference | 90th Annual Meeting of the International Association of Applied Mathematics and Mechanics |
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Abbreviated title | GAMM2019 |
Country/Territory | Austria |
City | Vienna |
Period | 18/02/19 → 22/02/19 |
Internet address |