|
[1]
|
M. Ainsworth and J. T. Oden, A Posteriori Error Estimation in Finite Element Analysis, Wiley-Interscience, New York, 2000.
doi: 10.1002/9781118032824.
|
|
[2]
|
I. Babuska and W. C. Rheinboldt, Error estimates for adaptive finite element computations, SIAM J. Numer. Anal., 15 (1978), 736-754.
doi: 10.1137/0715049.
|
|
[3]
|
G. Bao, G. Hu, J. Sun and T. Yin, Direct and inverse elastic scattering from anisotropic media, J. Math. Pures Appl., 117 (2018), 263-301.
doi: 10.1016/j.matpur.2018.01.007.
|
|
[4]
|
C. Bellis, F. Cakoni and B. B. Guzina, Nature of the transmission eigenvalue spectrum for elastic bodies, IMA J. Appl. Math., 78 (2013), 895-923.
doi: 10.1093/imamat/hxr070.
|
|
[5]
|
Ju. M. Berezanski$\breve{i}$, Expansions in Eigenfunctions of Selfadjoint Operators, Naukova Dumka, Kiev, 1965; English transl., Transl. Math. Monos., 17, Amer. Math. Soc., Providence, R.I., 1968.
|
|
[6]
|
L. Chen, IFEM: An Innovative Finite Element Methods Package in MATLAB, Technical Report, University of California at Irvine, 2009.
|
|
[7]
|
Z. Chen and R. Nochetto, Residual type a posteriori error estimates for elliptic obstacle problems, Numer. Math., 84 (2000), 527-548.
doi: 10.1007/s002110050009.
|
|
[8]
|
P. G. Ciarlet, Basic error estimates for elliptic problems, in: P. G. Ciarlet, J. L. Lions, (Ed.), Finite Element Methods (Part1), Handbook of Numerical Analysis, 2, Elsevier Science Publishers, North-Holand, 1991, 21–343.
|
|
[9]
|
X. Dai, J. Xu and A. Zhou, Convergence and optimal complexity of adaptive finite element eigenvalue computations, Numer. Math., 110 (2008), 313-355.
doi: 10.1007/s00211-008-0169-3.
|
|
[10]
|
S. Du and Z. Zhang, A robust residual-type a posteriori error estimator for convection-diffusion equations, J. Sci. Comput., 65 (2015), 138-170.
doi: 10.1007/s10915-014-9972-4.
|
|
[11]
|
B. Gong, J. Han, J. Sun and Z. Zhang, A shifted-inverse adaptive multigrid method for the elastic eigenvalue problem, Commun. Comput. Phys., 27 (2020), 251-273.
doi: 10.4208/cicp.OA-2018-0293.
|
|
[12]
|
J. Han and Y. Yang, An adaptive finite element method for the transmission eigenvalue problem, J. Sci. Comput., 69 (2016), 1279-1300.
doi: 10.1007/s10915-016-0234-5.
|
|
[13]
|
X. Ji, J. Sun and P. Li, Computation of interior elastic transmission eigenvalues using a conforming finite element and the secant method, Results Appli. Math., 5 (2020), Paper No. 100083, 12 pp.
doi: 10.1016/j.rinam.2019.100083.
|
|
[14]
|
H. Li and Y. Yang, An adaptive C$^{0}$IPG method for the Helmholtz transmission eigenvalue problem, Science China Mathematics, 61 (2018), 1519-1542.
doi: 10.1007/s11425-017-9334-9.
|
|
[15]
|
J. Maubach, Local bisection refinement for n-simplicial grids generated by reflection, SIAM J. Sci. Comput., 16 (1995), 210-227.
doi: 10.1137/0916014.
|
|
[16]
|
P. Morin, R.H. Nochetto and K. Siebert, Data oscillation and convergence of adaptive FEM, SIAM J. Numer. Anal., 38 (2000), 466-488.
doi: 10.1137/S0036142999360044.
|
|
[17]
|
Z. Shi and M. Wang, Finite Element Methods, Scientific Publishers, Beijing, 2013.
|
|
[18]
|
J. Sun and A. Zhou, Finite Element Methods for Eigenvalue Problems, Boca Raton, London, New York: CRC Press, Taylor & Francis, Group, 2016.
|
|
[19]
|
R. Verf$\ddot{u}$rth, A posteriori error estimators for the Stokes equations, Numer. Math., 55 (1989), 309-325.
doi: 10.1007/BF01390056.
|
|
[20]
|
R. Verf$\ddot{u}$rth, A posteriori error estimators for convection-diffusion equations, Numer. Math., 80 (1998), 641-663.
doi: 10.1007/s002110050381.
|
|
[21]
|
R. Verf$\ddot{u}$rth, A Review of a Posteriori Error Estimates and Adaptive Mesh-Refinement Techniques, Wiley-Teubner, New York, 1996.
|
|
[22]
|
Y. Xi, H. Geng and X. Ji, A $\rm {C^0IP}$ method of transmission eigenvalues for elastic waves, J. Comput. Phys., 374 (2018), 237-248.
doi: 10.1016/j.jcp.2018.07.053.
|
|
[23]
|
J. Xu and Z. Zhang, Analysis of recovery type a posteriori error estimators formildly structured grids, Math. Comput., 73 (2004), 1139-1152.
doi: 10.1090/S0025-5718-03-01600-4.
|
|
[24]
|
Y. Yang, J. Han and H. Bi, Error estimates and a two grid scheme for approximating transmission eigenvalues, preprint, arXiv: 1506.06486v2 [math.NA].
|
|
[25]
|
Y. Yang, J. Han and H. Bi, H$^{2}$-conforming methods and two-grid discretizations for the elastic transmission eigenvalue problem, Commun. Comput. Phys., 28 (2020), 1366-1388.
doi: 10.4208/cicp.OA-2019-0171.
|
|
[26]
|
Y. Yang, J. Han, H. Bi, H. Li and Y. Zhang, Mixed methods for the elastic transmission eigenvalue problem, Appli. Math. Comput., 374 (2020), 125081, 15 pp.
doi: 10.1016/j.amc.2020.125081.
|
|
[27]
|
Y. Yang, Y. Zhang and H. Bi, A type of adaptive C$^{0}$ non-conforming finite element method for the Helmholtz transmission eigenvalue problem, Comput. Methods Appli. Mech. Engrg., 360 (2020), 112697, 20 pp.
doi: 10.1016/j.cma.2019.112697.
|
|
[28]
|
O. Zienkiewicz and J. Zhu, The superconvergent patch recovery and a posteriori error estimates, Part 1: The recovery technique, Int. J. Numer. Methods Eng., 33 (1992), 1331-1364.
doi: 10.1002/nme.1620330702.
|
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