Self-adaptive strategy for one-dimensional finite element method based on EEP method with optimal super-convergence order  

作　　者：袁驷 邢沁妍 王旭 叶康生 

机构地区：[1]Key Laboratory Structural Engineering and Vibration of China Education Ministry,Department of Civil Engineering,Tsinghua University

出　　处：《Applied Mathematics and Mechanics(English Edition)》2008年第5期591-602,共12页应用数学和力学（英文版）

基　　金：the National Natural Science Foundation of China(No.50678093);Program for Changjiang Scholars and Innovative Research Team in University(No.IRT00736)

摘　　要：Based on the newly-developed element energy projection （EEP） method with optimal super-convergence order for computation of super-convergent results, an improved self-adaptive strategy for one-dimensional finite element method （FEM） is proposed. In the strategy, a posteriori errors are estimated by comparing FEM solutions to EEP super-convergent solutions with optimal order of super-convergence, meshes are refined by using the error-averaging method. Quasi-FEM solutions are used to replace the true FEM solutions in the adaptive process. This strategy has been found to be simple, clear, efficient and reliable. For most problems, only one adaptive step is needed to produce the required FEM solutions which pointwise satisfy the user specified error tolerances in the max-norm. Taking the elliptical ordinary differential equation of the second order as the model problem, this paper describes the fundamental idea, implementation strategy and computational algorithm and representative numerical examples are given to show the effectiveness and reliability of the proposed approach.Based on the newly-developed element energy projection （EEP） method with optimal super-convergence order for computation of super-convergent results, an improved self-adaptive strategy for one-dimensional finite element method （FEM） is proposed. In the strategy, a posteriori errors are estimated by comparing FEM solutions to EEP super-convergent solutions with optimal order of super-convergence, meshes are refined by using the error-averaging method. Quasi-FEM solutions are used to replace the true FEM solutions in the adaptive process. This strategy has been found to be simple, clear, efficient and reliable. For most problems, only one adaptive step is needed to produce the required FEM solutions which pointwise satisfy the user specified error tolerances in the max-norm. Taking the elliptical ordinary differential equation of the second order as the model problem, this paper describes the fundamental idea, implementation strategy and computational algorithm and representative numerical examples are given to show the effectiveness and reliability of the proposed approach.

关 键 词：finite element method （FEM） self-adaptive solution super-convergence optimal convergence order element energy projection condensed shape functions 

分 类 号：O242.21[理学—计算数学]