SIAM Journal on Scientific Computing, Volume 43, Issue 3, Page A1583-A1606, January 2021.
The aim of this paper is to study the numerical approximation of the displacement formulation of the acoustic eigenvalue problem in the axisymmetric case. We show that spurious eigenvalues appear when lowest order triangular Raviart--Thomas elements are used to discretize the problem. We propose an alternative weak formulation of the spectral problem which allows us to avoid this drawback. A finite element discretization based on the same finite elements is proposed and analyzed. Quasi-optimal order spectral convergence is proved, as well as absence of spurious modes. Numerical experiments are reported which agree with the theoretical results.

中文翻译：

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轴对称声振动问题位移公式的数值逼近

SIAM科学计算杂志，第43卷，第3期，第A1583-A1606页，2021
年1月。本文的目的是研究轴对称情况下声学特征值问题的位移公式的数值逼近。我们表明，当使用最低阶三角形Raviart-Thomas元素离散化问题时，会出现伪特征值。我们提出了频谱问题的另一种弱公式，可以使我们避免这一缺点。提出并分析了基于相同有限元的有限元离散化方法。证明了准最佳阶谱收敛，以及不存在杂散模式。报道了与理论结果相符的数值实验。