A multilevel preconditioner for the C-R FEM for elliptic problems with discontinuous coefficients  

作　　者：WANGFeng CHENJinRu HUANGpeiQi 

机构地区：[1]JiangsuKeyLaboratory,0rNSLSCS,SchoolofMathematicalSciences,NanjingNormalUniversity,Nanjing210046,China [2]DepartmentofAppliedMathematics,NanjingForestryUniversity,Nanjing210037,China

出　　处：《Science China Mathematics》2012年第7期1513-1526,共14页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China (Grant Nos.10871100 and 11071124)

摘　　要：In this paper, we propose a multilevel preconditioner for the Crouzeix-Raviart finite element approximation of second-order elliptic partial differential equations with discontinuous coefficients. Since the finite element spaces are nonnested, weighted intergrid transfer operators, which are stable under the weighted L2 norm, are introduced to exchange information between different meshes. By analyzing the eigenvalue distribution of the preconditioned system, we prove that except a few small eigenvalues, all the other eigenvalues are bounded below and above nearly uniformly with respect to the jump and the mesh size. As a result, we get that the convergence rate of the preconditioned conjugate gradient method is quasi-uniform with respect to the jump and the mesh size. Numerical experiments are presented to confirm our theoretical analysis.In this paper, we propose a multilevel preconditioner for the Crouzeix-Raviart finite element ap- proximation of second-order elliptic partial differential equations with discontinuous coefficients. Since the finite element spaces are nonnested, weighted intergrid transfer operators, which are stable under the weighted L2 norm, are introduced to exchange information between different meshes. By analyzing the eigenvalue distribu- tion of the preconditioned system, we prove that except a few small eigenvalues, all the other eigenvalues are bounded below and above nearly uniformly with respect to the jump and the mesh size. As a result, we get that the convergence rate of the preconditioned conjugate gradient method is quasi-uniform with respect to the jump and the mesh size. Numerical experiments are presented to confirm our theoretical analysis.

关 键 词：multilevel method Crouzeix-Raviart element discontinuous coefficients 

分 类 号：O241.82[理学—计算数学] TM561.506[理学—数学]