Stokes方程特征值问题自适应Crouzeix-Raviart有限元方法的收敛性分析  

CONVERGENCEOFADAPTIVE CROUZEIX-RAVIART FINITE ELEMENT METHOD FOR STOKES EIGENVALUE PROBLEMS

作　　者：沈玥 郑秀云[1] 王莹 Shen Yue;Zheng Xiuyun;Wang Ying(School of Science,Xi'an University of Architecture and Technology,Xi'an 710055)

机构地区：[1]西安建筑科技大学理学院,西安市710055

出　　处：《高等学校计算数学学报》2023年第4期341-370,共30页Numerical Mathematics A Journal of Chinese Universities

基　　金：国家自然科学基金(12301472,12201485);陕西省自然科学基金(2021JQ-493);陕西省教育厅科学研究计划自然科学专项(2021JQ-496).

摘　　要：0引言众所周知,特征值问题在许多科学和工程应用中起着重要的作用,如结构动力学,量子化学,磁流体动力学,控制理论(见[3,12,35])等.自适应有限元方法作为一种数值方法,源于其高效性和准确性,取得了巨大的成就[1,8,14,30].一个标准的自适应有限元算法一般具有如下循环流程:求解→估计→标记→加密.This paper focuses on the study of convergence and quasi-optimality of an adaptive Crouzeix-Raviart finite element method for Stokes eigenvalue problems.A posteriori error estimates with upper and lower bounds are first derived based on an equivalence of the approximations to eigenvalue problem and the associated boundary value problem.Then under mild assumption on the initial mesh,we prove the contraction property for the sum of the energy error of the eigenfunction and the scaled error estimator on two consecutive adaptive meshes,which also implies the convergence of the eigenvalue approximation.We finally show the quasi-optimal convergence rate of the adaptive algorithm.The paper ends with numerical experiments which confirm our theoretical analysis.

关 键 词：特征值问题 自适应有限元方法 STOKES方程 磁流体动力学 量子化学 结构动力学 收敛性分析 自适应有限元算法 

分 类 号：O241[理学—计算数学]