Meshless Galerkin analysis of the generalized Stokes problem
Meshless Galerkin analysis of the generalized Stokes problem
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DOI：
10.1016/j.camwa.2023.05.027
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发表时间：
2023-08
期刊：
影响因子：
--
通讯作者：
Xiaolin Li;Shuling Li
中科院分区：
文献类型：
--
作者：
Xiaolin Li;Shuling Li
本文提出并分析了一种稳定化无网格伽辽金法（EFG），用于广义Stokes问题的无网格伽辽金分析。针对无网格形函数缺乏插值性质的问题，采用Nitsche技巧，导出了广义Stokes问题的Nitsche型弱形式。通过引入基于残差的稳定化技术建立稳定化的Nitsch型EFG弱形式，该方法不仅允许速度和压力的等阶逼近空间，而且适用于小粘性大反应系数的广义Stokes问题.从理论上分析了稳定化EFG方法的inf-sup稳定性和误差估计。一些数值结果证明了该方法的有效性。
This paper proposes and analyzes a stabilized element-free Galerkin (EFG) method for meshless Galerkin analysis of the generalized Stokes problem. The Nitsche-type weak form of the generalized Stokes problem is derived by adopting Nitsche's technique to deal with the lack of interpolation property of meshless shape functions. By introducing the residual-based stabilization technique to establish a stabilized Nitsche-type EFG weak form, the proposed stabilized EFG method not only allows equal-order approximation spaces for velocity and pressure, but also applies to the generalized Stokes problem with small viscosity and large reaction coefficient. Both the inf-sup stability and the error estimation of the stabilized EFG method are analyzed theoretically. Some numerical results are provided to demonstrate the efficiency of the method.