主 题：A PRIORI AND A POSTERIORI ERROR ESTIMATES FOR QUASICONTINUUM APPROXIMATIONS
主讲人：四川大学副研究员、英国牛津大学博士 王皓
主持人：向开理 教授
时 间：2014年3月13日（星期四）下午4:40-5:40
地 点：柳林校区通博楼B412
主办单位：经济数学学院 科研处
主讲人简介：
王皓，四川大学副研究员，英国牛津大学数值分析学博士，主要研究领域是偏微分方程数值解、有限元方法及其自适应，目前主要从事计算材料学中原子／连续耦合方法建模与误差分析方面的研究。
内容提要：
This talk is on the error estimates of different energy based quasi continuum(QC)methods,which are a class of computational methods for the coupling of atomistic and continuum models for micro- or nano-scale materials.
The talk consists of two parts. The ?rst part considers the a priori error estimates of three energy based QC methods. The second part deals with the a posteriori error estimates of a speci?c energy based QC method which was recently developed.
In the ?rst part,we develop a uni?ed framework for the a priori error estimates and present a new and simpler proof based on negative-norme stimates,which essentially extends previous results.
In the second part, we establish the a posteriori error estimates for the newly developed energy based QC method for an energy norm and for the total energy. The analysis is based on a posteriori residual and stability estimates. Adaptive mesh re?nement algorithms based on these error estimators are formulated.
In both parts, numerical experiments are presented to illustrate the results of our analysis and indicate the optimal convergence rates.
