Paper Info
Title
Higher order stable generalized finite element method for the elliptic eigenvalue and source problems with an interface in 1D
Abstract
We study the generalized finite element methods (GFEMs) for the second-order elliptic eigenvalue problem with an interface in 1D. The linear stable generalized finite element methods (SGFEM) were recently developed for the elliptic source problem with interfaces. We first generalize SGFEM to arbitrary order elements and establish the optimal error convergence of the approximate solutions for the elliptic source problem with an interface. We then apply the abstract theory of spectral approximation of compact operators to establish the error estimation for the eigenvalue problem with an interface. The error estimations on eigenpairs strongly depend on the estimation of the discrete solution operator for the source problem. We verify our theoretical findings in various numerical examples including both source and eigenvalue problems.
Year
DOI
Venue
2020
10.1016/j.cam.2019.112558
Journal of Computational and Applied Mathematics
Keywords
Field
DocType
Interface problem,Eigenvalue problem,FEM,SGFEM
Convergence (routing),Mathematical analysis,Finite element method,Compact operator,Operator (computer programming),Spectral approximation,Mathematics,Eigenvalues and eigenvectors
Journal
Volume
ISSN
Citations 
368
0377-0427
0
PageRank 
References 
Authors
0.34
0
2
Name
Order
Citations
PageRank
Quanling Deng100.34
Victor M. Calo219138.14