势问题的无单元Galerkin方法的误差估计  

Error estimates of element-free Galerkin method for potential problems

作　　者：程荣军[1] 程玉民[1] 

机构地区：[1]上海大学上海市应用数学和力学研究所

出　　处：《物理学报》2008年第10期6037-6046,共10页Acta Physica Sinica

基　　金：国家自然科学基金(批准号:10571118);上海市重点学科建设项目(批准号:Y0103)资助的课题~~

摘　　要：在高维情况下,首先研究了无单元Galerkin方法的形函数构造方法——移动最小二乘法在Sobolev空间Wk,p(Ω)中的误差估计.然后,在势问题的无单元Galerkin方法的基础上,研究了势问题的通过罚函数法施加本质边界条件的无单元Galerkin方法在Sobolev空间中的误差估计.当节点和形函数满足一定条件时,证明了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半径密切相关.最后,通过算例验证了结论的正确性.The error estimates for moving least-square approximation, which is the method for obtaining the shape function in elementfree Galerkin method, are presented in Sobolev space W^k,p （f2） for high dimensional problems. Then on the basis of elementfree Galerkin method for potential problems, the error estimates for element-free Galerkin method for potential problems, in which the essential boundary conditions are enforced by penalty methods, are obtained. The error estimates we present in this paper have optimal order when the nodes and shape functions satisfy certain conditions. From the error analysis, it is shown that the error bound of the potential problem is directly related to the radii of the weight functions. Two numerical examples are also given to verify the conclusions in this paper.

关 键 词：无网格方法 无单元Galerkin方法 势问题 误差估计 

分 类 号：O411[理学—理论物理]