New Higher-Order Mass-Lumped Tetrahedral Elements for Wave Propagation Modelling

Sjoerd Geevers, W.A. Mulder, Jacobus J.W. van der Vegt

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    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 Read More:
    Original languageEnglish
    Pages (from-to)A2830 - A2857
    Number of pages28
    JournalSIAM journal on scientific computing
    Issue number5
    Publication statusPublished - 11 Sept 2018


    • Mass lumping
    • Tetrahedral elements
    • Spectral element method
    • Wave equation

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