弹性力学的无单元Galerkin方法的误差估计

摘要

基于移动最小二乘法在Sobolev空间W^k.p（Ω）中的误差估计以及弹性力学问题的变分弱形式中出现的双线性形式的连续性和强制性，研究了弹性力学问题的无单元Galerkin方法的误差分析以及数值解的误差和影响域半径之间的关系，给出了弹性力学问题的无单元Galerkin方法在Sobolev空间中的误差估计定理，并证明了当节点和形函数满足一定条件时该误差估计是最优阶的．从误差分析中可以看出，数值解的误差与权函数的影响域半径密切相关．最后，通过算例验证了结论的正确性．%Based on both the error estimates of moving least-square approximation in the Sobolev space W^k.P（,O） and the continuity and coercion of the bi-linearity in the weak form of the elasticity, the error analysis of element-free Galerkin method for elasticity is discussed in this paper, the relationship between the error and the radius of the weight function is given, and the theorem of the error estimate presented. The error estimate proves to be of optimal order when nodes and shape functions satisfy some conditions. From the error analysis, it is shown that the error bound of the elasticity is directly related to the radius of the weight function. And a numerical example is given to verify the correctness of the given results.