A new weak Galerkin finite element method for the Helmholtz equation
A new weak Galerkin finite element method for the Helmholtz equation
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DOI：
10.1093/imanum/dru026
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发表时间：
2015-07
影响因子：
2.1
通讯作者：
Lin Mu;Junping Wang;X. Ye
中科院分区：
文献类型：
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作者：
Lin Mu;Junping Wang;X. Ye
介绍并分析了亥姆霍兹方程的一种绝对稳定弱伽辽金有限元法。这意味着对于任何波数k，该方法的稳定性和适定性都可以在没有网格尺寸约束的情况下得到。该方法是将离散弱梯度算子应用于由二维多边形或三维多面体组成的具有一定形状规律性的有限元分区上的不连续分段多项式。对于这些弱Galerkin有限元解，建立了离散H1和L2范数的误差估计。数值算例验证了理论的正确性。
An absolutely stable weak Galerkin finite element method is introduced and analyzed for the Helmholtz equation. This means that the stability and well posedness of the method for any wave number k can be derived without mesh size constraint. This method is designed by using a discrete weak gradient operator applied to discontinuous piecewise polynomials on finite element partitions consisting of polygons in two dimensions or polyhedra in three dimensions with certain shape regularity. Error estimates in both discrete H1 and L2 norms are established for these weak Galerkin finite element solutions. Numerical examples are tested to support the theory.