New higher-order mass-lumped tetrahedral elements for wave propagation modelling

Journal article (2018)

Authors

S. Geevers University of Twente
W.A. Mulder Shell Global Solutions International B.V., Applied Geophysics and Petrophysics - CEG
J. J.W. van der Vegt University of Twente
Research Group
Applied Geophysics and Petrophysics (CEG) (TU Delft)
Copyright: © 2018 S. Geevers, W.A. Mulder, J. J.W. van der Vegt
DOI: https://doi.org/10.1137/18M1175549
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Published Date

2018

Language

English

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Faculty

Civil Engineering & Geosciences

Department

Geoscience and Engineering

Research Group

Applied Geophysics and Petrophysics

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 until now. We prove that our accuracy condition results in a mass-lumped finite element method that converges with optimal order in the $L^2$-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.

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