NEW HIGHER-ORDER MASS-LUMPED TETRAHEDRAL ELEMENTS FOR WAVE PROPAGATION MODELLING

被引：25

作者：

Geevers, S. ^{[1
]}

Mulder, W. A. ^{[2
,3
]}

Van der Vegt, J. J. W. ^{[1
]}

机构：

[1] Univ Twente, Dept Appl Math, NL-7500 AE Enschede, Netherlands

[2] Shell Global Solut Int BV, NL-1031 HW Amsterdam, Netherlands

[3] Delft Univ Technol, NL-2628 CD Delft, Netherlands

来源：

SIAM JOURNAL ON SCIENTIFIC COMPUTING | 2018年 / 40卷 / 05期

关键词：

mass lumping; tetrahedral elements; spectral element method; wave equation; FINITE-ELEMENTS; EQUATION; SCHEMES;

D O I：

10.1137/18M1175549

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：A2830 / A2857

页数：28

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