A weak Galerkin mixed finite element method for the Helmholtz equation with large wave numbers
A weak Galerkin mixed finite element method for the Helmholtz equation with large wave numbers
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DOI：
10.1002/num.22242
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发表时间：
2018-05
影响因子：
3.9
通讯作者：
Ruishu Wang;Xiaoshen Wang;Q. Zhai;Kai Zhang
中科院分区：
文献类型：
--
作者：
Ruishu Wang;Xiaoshen Wang;Q. Zhai;Kai Zhang
本文介绍并分析了大波数亥姆霍兹方程的一种新的弱伽辽金混合有限元方法。对于任意波数k，在没有网格尺寸约束的情况下，建立了该方法的稳定性和适定性。弱伽辽金混合方法由于允许使用间断逼近函数，因而对逼近和网格的限制较少，因而具有很高的灵活性。在弱Galerkin混合有限元列式中，逼近函数可以是不同阶的分段多项式，网格可以由不同形状的单元组成。对于弱Galerkin混合有限元解，建立了离散H1和L2模下的次优阶误差估计.数值算例验证了理论的正确性。
In this article, a new weak Galerkin mixed finite element method is introduced and analyzed for the Helmholtz equation with large wave numbers. The stability and well‐posedness of the method are established for any wave number k without mesh size constraint. Allowing the use of discontinuous approximating functions makes weak Galerkin mixed method highly flexible in term of little restrictions on approximations and meshes. In the weak Galerkin mixed finite element formulation, approximation functions can be piecewise polynomials with different degrees on different elements and meshes can consist elements with different shapes. Suboptimal order error estimates in both discrete H1 and L2 norms are established for the weak Galerkin mixed finite element solutions. Numerical examples are tested to support the theory.