Weak Galerkin finite element method for linear elasticity interface problems
Weak Galerkin finite element method for linear elasticity interface problems
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DOI：
10.1016/j.amc.2022.127589
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发表时间：
2023-02
期刊：
影响因子：
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通讯作者：
Hui Peng;Ruishu Wang;Xiuli Wang;Yongkui Zou
中科院分区：
文献类型：
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作者：
Hui Peng;Ruishu Wang;Xiuli Wang;Yongkui Zou
本文将弱伽辽金有限元法应用于线弹性界面模型。由于解在穿过界面时可能变得不连续，我们首先在界面上用双值弱函数离散模型。然后，为了便于理论分析和算法实现，我们将界面条件代入弱Galerkin公式，构造了一个在界面上具有单值函数的弱Galerkin方法.进一步证明了弱Galerkin格式的适定性，并给出了能量模和L2模的先验误差估计.最后，我们提出了一些数值实验来证明我们的方法的效率和锁定的自由属性。
In this paper, we apply a weak Galerkin finite element method to a linear elasticity interface model. Since the solution may become discontinuous while crossing the interface, we first discretize the model by double-valued weak functions on the interface. Then, in order to facilitate theoretical analysis and algorithm implementation, we substitute interface conditions into the weak Galerkin formulation and construct a weak Galerkin method with single-valued functions on the interface. Furthermore, we prove the well-posedness of the weak Galerkin scheme and derive a priori error estimates in energy norm and L 2 norm. Finally, we present some numerical experiments to demonstrate the efficiency and the locking-free property of our method.