中文摘要：

复变量移动最小二乘近似是形成无网格法形函数的重要方法，为了研究相应的无网格方法的误差估计，需要先分析复变量移动最小二乘近似的逼近误差．首先介绍了复变量移动最小二乘近似，接着在权函数满足一定假设的条件下，详细讨论了复变量移动最小二乘近似逼近函数在Sobolev空间中的误差估计，给出了逼近函数在∥范数下的误差界，分析结果表明逼近函数的误差随着节点间距的减小而降低．最后给出了一个数值算例来验证理论分析的正确性．

英文摘要：

The complex variable moving least square （CVMLS） approximation is an important approach to construct shape functions in the meshless method. For the error analysis of the CVMLS-based meshless method, it is fundamental to conduct error estimates of the CVMLS ap- proximation in Sobolev spaces. First an introduction of the CVMLS was given. Then, the error estimates of the CVMLS in Sobolev spaces with weight functions satisfying specific conditions were obtained. The error bounds of the approximation functions in Hk norm were given. Finally, a numerical example was given to verify the validity of the theoretical analysis. The results show that the errors will decrease as the nodal spacings reduce.