A Trefftz-discontinuous Galerkin method for time-harmonic elastic wave problems

被引：4
作者：
Yuan, Long [1 ]
Liu, Yang [2 ]
机构：
[1] Shandong Univ Sci & Technol, Coll Math & Syst Sci, Qingdao 266590, Shandong, Peoples R China
[2] Inst Appl Phys & Computat Math, Beijing 100094, Peoples R China
来源：
COMPUTATIONAL & APPLIED MATHEMATICS | 2019年 / 38卷 / 03期
关键词：
Elastic waves; Nonhomogeneous; Local spectral element; Plane wave discontinuous Galerkin; Plane wave basis functions; Error estimates; 65N30; 65N55; WEAK VARIATIONAL FORMULATION; PREASYMPTOTIC ERROR ANALYSIS; HELMHOLTZ-EQUATION; MAXWELLS EQUATIONS; PLANE-WAVES; CIP-FEM; ELEMENTS; PROPAGATION; SCATTERING;
D O I：
10.1007/s40314-019-0900-y
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we develop a plane wave discontinuous Galerkin method combined with local spectral element method for the elastic wave propagation in two and three space dimensions. We derive the error estimates of the approximation solutions in the mesh-dependent norm and the mesh-independent norm. Some dependence of the error bounds on the orders q of local spectral elements and the number p of plane wave propagation directions is given. Numerical results assess the validity of the theoretical results and indicate that the resulting approximate solutions generated by the PWDG-LSFE possess high accuracy.
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页数：29
相关论文
共 40 条
[1]  
[Anonymous], 2003, Finite Element Methods for Maxwell's Equations
[2]  
Auld B., 1973, Acoustic Waves and Fields in Solids
[3]   ERROR ESTIMATES FOR THE ULTRA WEAK VARIATIONAL FORMULATION OF THE HELMHOLTZ EQUATION [J].
Buffa, Annalisa ;
Monk, Peter .
ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE, 2008, 42 (06) :925-940
[4]   Using plane waves as base functions for solving time harmonic equations with the ultra weak variational formulation [J].
Cessenat, O ;
Després, B .
JOURNAL OF COMPUTATIONAL ACOUSTICS, 2003, 11 (02) :227-238
[5]   Application of an ultra weak variational formulation of elliptic PDEs to the two-dimensional Helmholtz problem [J].
Cessenat, O ;
Despres, B .
SIAM JOURNAL ON NUMERICAL ANALYSIS, 1998, 35 (01) :255-299
[6]  
Cessenat O., 1996, THESIS
[7]   Sharp-regularity coefficient estimates for complex-valued acoustic and elastic Helmholtz equations [J].
Cummings, P ;
Feng, XB .
MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES, 2006, 16 (01) :139-160
[8]   PREASYMPTOTIC ERROR ANALYSIS OF HIGHER ORDER FEM AND CIP-FEM FOR HELMHOLTZ EQUATION WITH HIGH WAVE NUMBER [J].
Du, Yu ;
Wu, Haijun .
SIAM JOURNAL ON NUMERICAL ANALYSIS, 2015, 53 (02) :782-804
[9]   Improvement of PUFEM for the numerical solution of high-frequency elastic wave scattering on unstructured triangular mesh grids [J].
El Kacimi, A. ;
Laghrouche, O. .
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, 2010, 84 (03) :330-350
[10]   Numerical modelling of elastic wave scattering in frequency domain by the partition of unity finite element method [J].
El Kacimi, A. ;
Laghrouche, O. .
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, 2009, 77 (12) :1646-1669
1234