Sobolev方程的POD降维H^(1)-Galerkin混合有限元分裂格式  

Proper Orthogonal Decomposition Reduced-order H^(1)-Galerkin Mixed Finite Element Splitting Scheme for the Sobolev Equation

作　　者：王懿晖 何斯日古楞 张婷[1] WANG Yihui;HE Siriguleng;ZHANG Ting(School of Mathematical Sciences,Inner Mongolia University,Hohhot O10021,China;Hohhot Minzu College,Hohhot 010051,China)

机构地区：[1]内蒙古大学数学科学学院,呼和浩特010021 [2]呼和浩特民族学院,呼和浩特010051

出　　处：《内蒙古大学学报（自然科学版）》2022年第5期462-467,共6页Journal of Inner Mongolia University：Natural Science Edition

基　　金：国家自然科学基金(12161034);呼和浩特民族学院科研创新建设计划项目资助。

摘　　要：基于Sobolev方程的H^(1)-Galerkin混合有限元分裂格式的矩阵形式,利用特征正交分解技术,建立一种降维模型,并用矩阵分析法证明了降维格式的收敛性。最后,通过数值算例验证了理论分析的正确性和降维模型的可行性和有效性。A reduced-order numerical model is established based on matrix form of the H^(1)-Galerkin mixed finite element splitting format of one-dimensional Sobolev equation and the proper orthogonal decomposition technique.The convergence of the reduced-order format is proved by matrix analysis.Finally,the correctness of the theoretical analysis and the feasibility and validity of the reduced-order model are verified by some numerical examples.

关 键 词：SOBOLEV方程 特征正交分解 H^(1)-Galerkin混合有限元分裂格式 收敛性分析 

分 类 号：O241.82[理学—计算数学]