有限元先验与后验误差估计中常数的精细估计及其应用

项目名称： 有限元先验与后验误差估计中常数的精细估计及其应用

项目编号： No.11526078

项目类型： 专项基金项目

立项/批准年度： 2016

项目学科： 数理科学和化学

项目作者： 陈红如

作者单位： 河南工业大学

项目金额： 3万元

中文摘要： 有限元误差分析中的常数有插值误差常数、逆不等式常数、迹定理常数、混合元方法的inf-sup常数和非协调元的相容误差常数等等。如果能比较精细的估计出这些常数的取值范围，那么将对定量估计有限元的误差很有帮助。近年来，这方面的研究也开始引起人们的注意。目前，已经有一些粗糙的分散的研究成果。本项目旨在研究有限元误差估计中常数的精细估计。目的是对有限元误差估计中的各种常数做一个全面的、系统的研究，找到精细估计这些常数的简洁有效的方法，得到更为精确的有限元误差。这样，就能更加有效的把握具体的有限元误差，以便得到更有效的有限元算法。尤其，这种对常数的精细估计可以广泛应用到有限元的后验误差估计当中，得到完全可计算的后验误差估计子。而后验误差估计是自适应有限元的理论基础，这就可以更好地发挥自适应有限元方法的优越性。

中文关键词： 有限元方法；显示误差估计；常数的界；后验误差估计；

英文摘要： As is known that there appear various constants in the process to derive the error estimates, such as : interpolation error constants; constants in the inverse inequalities; constants in trace theorem; the discrete inf-sup constants for mixed finite elements and the consistency error constants for nonconforming finite elements and so on. It is good to evaluate these constants explicitly for a quantitative error bound purpose. In recent years, this subject began to arouse people's attention. At present, there have been some scattered research results on this subject. In this project, we study the sharp estimation of the constants in the error estimates of finite element method. we are aim to find an effective method to estimate these constants after a comprehensive and systematic research on the above constants, and then, to get the more accurate finite element error. Therefore, we can more effectively control the error of finite element for getting more effective finite element method. Especially, such highly accurate approximate values for these constants can be widely used for a priori and a posteriori error estimations in adaptive computation and numerical verification of finite element solutions, then, we can obtain fully computable posteriori error estimator. As a result, it can better play the advantages o

英文关键词： Finite element method；Explicit error estimates；Bound of the constants；Posteriori error estimates；