Semi and fully discrete error analysis for elastodynamic interface problems using immersed finite element methods
Semi and fully discrete error analysis for elastodynamic interface problems using immersed finite element methods
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DOI：
10.1016/j.camwa.2023.07.014
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发表时间：
2023-08-03
影响因子：
2.9
通讯作者：
Zhang，Xu
中科院分区：
文献类型：
--
作者：
Chen，Yuan;Hou，Songming;Zhang，Xu
在本文中，我们提出了一种用于解决界面未拟合网格上的弹性动力学界面问题的浸入式有限元（IFE）方法。对于空间离散化，我们使用向量值 P 1 和 Q 1 IFE 空间。我们建立了这些 IFE 空间的一些重要属性，例如逆不等式，这对于误差分析至关重要。对于时间离散化，推导了半离散和全离散方案。所提出的方案被证明是无条件稳定的，并且在能量、L 2 和半H 1 范数上具有最优收敛速度。数值例子旨在验证我们的理论分析并证明我们方案的稳定性和鲁棒性。
In this paper, we present an immersed finite element (IFE) method for solving the elastodynamics interface problems on interface-unfitted meshes. For spatial discretization, we use vector-valued P 1 and Q 1 IFE spaces. We establish some important properties of these IFE spaces, such as inverse inequalities, which will be crucial in the error analysis. For temporal discretization, both the semi-discrete and the fully discrete schemes are derived. The proposed schemes are proved to be unconditionally stable and enjoy optimal rates of convergence in the energy, L 2 and semi-H 1 norms. Numerical examples are designed to verify our theoretical analysis and to demonstrate the stability and robustness of our schemes.