圆域上Steklov资源问题有效的谱Galerkin逼近和误差估计  

Efficient spectral Galerkin approximation and error estimation for Steklov resource problem on circular domain

作　　者：周晓军 谭婷 ZHOU Xiaojun;TAN Ting(School of Mathematical Science,Guizhou Normal University,Guiyang,Guizhou 550025,China)

机构地区：[1]贵州师范大学数学科学学院,贵州贵阳550025

出　　处：《贵州师范大学学报（自然科学版）》2021年第5期60-66,共7页Journal of Guizhou Normal University：Natural Sciences

基　　金：国家自然科学基金(批准号:11661022);贵州师范大学博士科研基金(No.11904-0516022)资助项目。

摘　　要：提出了圆域上Steklov资源问题一种基于降维格式的谱Galerkin逼近。首先,利用极坐标变换把原问题化为一系列独立的一维问题,从而可以并行求解。然后,引入了极条件和适当的带权Sobolev空间,建立了弱形式和相应的离散格式。再结合带权Sobolev空间中投影算子的逼近性质,证明了逼近解的误差估计。最后,给出了一些数值例子,数值结果表明了算法的有效性和理论结果的正确性。A spectral Galerkin approximation based on reduced dimension scheme for Steklov resource problem on circular domain is proposed.First of all,the original problem is transformed into a series of independent one-dimensional problems by polar coordinate transformation,which can be solved in parallel.Then,by introducing the polar condition and the appropriate weighted Sobolev space,the weak form and the corresponding discrete scheme are established.Combined with the approximation properties of projection operators in weighted Sobolev spaces,the error estimates of approximation solutions are proved.Finally,some numerical examples are given to show the effectiveness of the algorithm and the correctness of the theoretical results.

关 键 词：Steklov资源问题 带权的Sobolev空间 谱Galerkin逼近 误差估计 圆形区域 

分 类 号：O241.1[理学—计算数学]