In this paper we analyze a mixed displacement-pseudostress formulation for the elasticity eigenvalue problem. We propose a finite element method to approximate the pseudostress tensor with Raviart-Thomas elements and the displacement with piecewise polynomials. With the aid of the classic theory for compact operators, we prove that our method is convergent and does not introduce spurious modes. Also, we obtain error estimates for the proposed method. Finally, we report some numerical tests supporting the theoretical results.
翻译:在本文中,我们分析了一种混合的变位-假假体配方,用于应对弹性值问题。我们提出了一个有限的元素方法,以拉维阿尔特-图马斯元素比喻假体压力成像,以片状多元体元素比喻离位。我们借助对紧凑操作者的经典理论,证明我们的方法是趋同的,没有引入虚假的模式。此外,我们获得了对拟议方法的误差估计。最后,我们报告了一些支持理论结果的数字测试。