Consistent pseudo-derivatives in meshless methods
Consistent pseudo-derivatives in meshless methods
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DOI：
10.1016/s0045-7825(96)01234-0
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发表时间：
1997-07
影响因子：
7.2
通讯作者：
Y. Krongauz;T. Belytschko
中科院分区：
文献类型：
--
作者：
Y. Krongauz;T. Belytschko
开发了无网格 Petrov-Galerkin 公式，其中试验函数的导数作为 Shepard 函数导数的线性组合获得。一个关键贡献是为 Petrov-Galerkin 方法开发了不可积伪导数的测试函数和试验函数条件，并通过了补丁测试。数值结果表明，所得到的方法比采用 Shepard 近似的 Galerkin 方法更加精确，并且超过了线性有限元的收敛速度。
A meshless Petrov-Galerkin formulation is developed in which derivatives of the trial functions are obtained as a linear combination of derivatives of Shepard functions. A key contribution is the development of conditions on test functions and trial functions for nonintegrable pseudo-derivatives for Petrov-Galerkin method which pass the patch test. Numerical results show that the resulting method is substantially more accurate than the Galerkin method with Shepard approximants and exceeds the rate of convergence of linear finite elements.