A NEW FINITE ELEMENT SPACE FOR EXPANDED MIXED FINITE ELEMENT METHOD  

作　　者：Jing Chen Zhaojie Zhou Huanzhen Chen Hong Wang 

机构地区：[1]School of Economics,Shandong Normal University,Jinan 250014,China [2]School of Mathematics and Statistics,Shandong Normal University,Jinan 250014,China [3]Department of Mathematics,University of South Carolina,Columbia,South Carolina 29208,USA

出　　处：《Journal of Computational Mathematics》2023年第5期817-840,共24页计算数学（英文）

基　　金：supported by NSF of China grant 11971276;H.Chen was supported by NSF of China grants 12171287,10971254 and 11471196;H.Wang was supported by the ARO MURI Grant W911NF-15-1-0562;by the National Science Foundation under Grant DMS-2012291.

摘　　要：In this article,we propose a new finite element spaceΛh for the expanded mixed finite element method(EMFEM)for second-order elliptic problems to guarantee its computing capability and reduce the computation cost.The new finite element spaceΛh is designed in such a way that the strong requirement V h⊂Λh in[9]is weakened to{v h∈V h;d i v v h=0}⊂Λh so that it needs fewer degrees of freedom than its classical counterpart.Furthermore,the newΛh coupled with the Raviart-Thomas space satisfies the inf-sup condition,which is crucial to the computation of mixed methods for its close relation to the behavior of the smallest nonzero eigenvalue of the stiff matrix,and thus the existence,uniqueness and optimal approximate capability of the EMFEM solution are proved for rectangular partitions in R d,d=2,3 and for triangular partitions in R 2.Also,the solvability of the EMFEM for triangular partition in R 3 can be directly proved without the inf-sup condition.Numerical experiments are conducted to confirm these theoretical findings.

关 键 词：New finite element space Expanded mixed finite element Minimum degrees of freedom The inf-sup condition SOLVABILITY Optimal convergence. 

分 类 号：O241.82[理学—计算数学]