Two-scale sparse finite element approximations  

作　　者：LIU Fang ZHU JinWei 

机构地区：[1]School of Statistics and Mathematics,Central University of Finance and Economics [2]The State Key Laboratory of Scientific and Engineering Computing,Institute of Computational Mathematics and Scientific,Engineering Computing,Academy of Mathematics and Systems Science,Chinese Academy of Sciences

出　　处：《Science China Mathematics》2016年第4期789-808,共20页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China(Grant Nos.10971059,11071265 and 11171232);the Funds for Creative Research Groups of China(Grant No.11021101);the National Basic Research Program of China(Grant No.2011CB309703);the National Center for Mathematics and Interdisciplinary Sciences,Chinese Academy of Sciences;the Program for Innovation Research in Central University of Finance and Economics

摘　　要：To reduce computational cost,we study some two-scale finite element approximations on sparse grids for elliptic partial differential equations of second order in a general setting.Over any tensor product domain ?R^d with d = 2,3,we construct the two-scale finite element approximations for both boundary value and eigenvalue problems by using a Boolean sum of some existing finite element approximations on a coarse grid and some univariate fine grids and hence they are cheaper approximations.As applications,we obtain some new efficient finite element discretizations for the two classes of problem:The new two-scale finite element approximation on a sparse grid not only has the less degrees of freedom but also achieves a good accuracy of approximation.To reduce computational cost,we study some two-scale finite element approximations on sparse grids for elliptic partial differential equations of second order in a general setting.Over any tensor product domain ？R^d with d = 2,3,we construct the two-scale finite element approximations for both boundary value and eigenvalue problems by using a Boolean sum of some existing finite element approximations on a coarse grid and some univariate fine grids and hence they are cheaper approximations.As applications,we obtain some new efficient finite element discretizations for the two classes of problem：The new two-scale finite element approximation on a sparse grid not only has the less degrees of freedom but also achieves a good accuracy of approximation.

关 键 词：combination discretization eigenvalue finite element postprocessing two-scale 

分 类 号：O241.5[理学—计算数学]