四阶Steklov资源问题有效的谱Galerkin逼近及误差估计  

Efficient spectral-galerkin approximation and error estimation for fourth-order steklov resource problem

作　　者：郑继会 田晓红 安静 ZHENG Jihui;TIAN Xiaohong;AN Jing(School of Mathematical Science,Guizhou Normal University,Guiyang 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：《南昌大学学报（理科版）》2023年第6期511-518,共8页Journal of Nanchang University(Natural Science)

基　　金：国家自然科学基金资助项目(12061023)。

摘　　要：提出了四阶Steklov资源问题的一种有效的谱Galerkin逼近及误差估计。首先引入了适当的Sobolev空间,推导了原问题的弱形式及相应的离散格式。其次,基于Lax-Milgram引理,证明了弱解和逼近解的存在唯一性,再根据正交投影算子的逼近性质,进一步证明了逼近解的误差估计。另外构造了逼近空间中的一组基函数,推导了离散格式基于张量积的矩阵形式。最后给出了一些数值算例,数值结果表明了该算法的有效性和理论结果的正确性。This paper proposed an efficient spectral-Galerkin approximation and error estimation for the fourth-order Steklov resource problem.Firstly,an appropriate Sobolev space was introduced and the weak form of the original problem,along with its corresponding discrete formulation,was derived.Secondly,the existence and uniqueness of the weak solution and the approximation solution were proven based on the Lax-Milgram lemma.Furthermore,error estimates for the approximation solution were demonstrated by using the approximation properties of the orthogonal projection operators.Additionally,a set of appropriate basis functions in the approximation space was constructed and the matrix form of the discrete scheme based on tensor product was derived.Finally,some numerical examples were given to show the effectiveness of the algorithm and the correctness of the theoretical results.

关 键 词：四阶Steklov资源问题 谱Galerkin方法 误差估计 张量积 

分 类 号：O241.82[理学—计算数学]