| Poisson方程的混合无网格方法(英文) |
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| 引用本文： | 雷俊丽.Poisson方程的混合无网格方法(英文)[J].应用数学,2010,23(1). |
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| 作者姓名： | 雷俊丽 |
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| 作者单位： | 湖北经济学院统计与应用数学系,湖北,武汉,430205 |
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| 摘 要： | 以Poisson方程的混合变分形式为基础,采用移动最小二乘方法建立插值形函数空间,给出了Poisson方程的混合无网格方法,理论上证明了Poisson方程混合无网格解的存在唯一性,并给出了误差估计.本质边界条件的处理采用Lagrange乘子法.数值算例表明,在应用相同阶次的基函数条件下,利用混合无网格方法求解Poisson方程所得的解的梯度值优于传统的无网格方法及有限元法.
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| 关 键 词： | Poisson方程 混合变分形式 移动最小二乘法 混合无网格法 |
The Mixed Meshfree Method for Poisson Equation |
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| LEI Jun-li.The Mixed Meshfree Method for Poisson Equation[J].Mathematica Applicata,2010,23(1). |
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| Authors: | LEI Jun-li |
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| Abstract: | By using moving least square(MLS) shape functions and based on the mixed variational priciple,a mixed meshfree method for Poisson equation is established. The existence and uniqueness of this method for Poisson equation is proved and the error estimate is provided. Compared with the traditional element free Galerkin(EFG) method and the finite element method(FEM), some numerical examples illustrate that the method obtains higher accuracy in obtaining the gradient of the original variable of the problem when the basis function has the same order. |
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| Keywords: | Poisson equation Moving least square Mixed meshfree method |
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