降阶单元的新进展:内置了最大模误差估计器的自适应有限元法初探  

NEW PROGRESS IN REDUCED ELEMENT:AN ADAPTIVE FINITE ELEMENT METHOD WITH BUILT-IN ERROR ESTIMATOR IN MAXIMUM NORM

作　　者：袁驷[1] 杨帅[1] 袁全 王亦平 YUAN Si;YANG Shuai;YUAN Quan;WANG Yi-ping(Department of Civil Engineering,Tsinghua University,Key Laboratory of Civil Engineering Safety and Durability of China Education Ministry,Beijing 100084,China)

机构地区：[1]清华大学土木工程系,土木工程安全与耐久教育部重点实验室,北京100084

出　　处：《工程力学》2024年第3期1-8,共8页Engineering Mechanics

基　　金：国家自然科学基金项目(51878383,51378293)。

摘　　要：该文基于初值问题中降阶单元的成功实践,进一步对一般边值问题提出无需超收敛计算、无需结构化网格、无需结点位移修正的降阶单元;进而提出以降阶单元作为最终解,且内置了最大模误差估计器的自适应有限元算法。该文对这一研究进展做简要介绍,并给出一维和二维边值问题的初步算例,以展示本法的可行性、有效性和可靠性。Based on the successful performance of the reduced element for initial value problems,the reduced element for general boundary value problems is proposed without the needs for super-convergence calculations,structural meshes and nodal accuracy improvement.An adaptive finite element algorithm with the solution of the reduced element and a built-in maximum norm error estimator as the final results is subsequently proposed.This paper gives a brief report to this research progress and provides preliminary numerical examples in one-and twodimensional boundary value problems to exhibit the feasibility,effectiveness and reliability of the proposed algorithm.

关 键 词：有限元法 边值问题 降阶单元 最大模 自适应有限元法 

分 类 号：O342[理学—固体力学]