Geodesic
Nonconforming finite element approximations of the Steklov eigenvalue problem and its lower bound approximations
Applications of Mathematics, Tome 58 (2013) no. 2, pp. 129-151

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

The paper deals with error estimates and lower bound approximations of the Steklov eigenvalue problems on convex or concave domains by nonconforming finite element methods. We consider four types of nonconforming finite elements: Crouzeix-Raviart, $Q_{1}^{\rm rot}$, $EQ_{1}^{\rm rot}$ and enriched Crouzeix-Raviart. We first derive error estimates for the nonconforming finite element approximations of the Steklov eigenvalue problem and then give the analysis of lower bound approximations. Some numerical results are presented to validate our theoretical results.
DOI : 10.1007/s10492-013-0007-5
Classification : 35A35, 35J25, 35P10, 35P15, 65N12, 65N15, 65N25, 65N30
Keywords: Steklov eigenvalue problem; nonconforming finite element; error estimate; lower bound of the eigenvalues 
@article{10_1007_s10492_013_0007_5,
     author = {Li, Qin and Lin, Qun and Xie, Hehu},
     title = {Nonconforming finite element approximations of the {Steklov} eigenvalue problem and its lower bound approximations},
     journal = {Applications of Mathematics},
     pages = {129--151},
     publisher = {mathdoc},
     volume = {58},
     number = {2},
     year = {2013},
     doi = {10.1007/s10492-013-0007-5},
     mrnumber = {3034819},
     zbl = {1274.65296},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1007/s10492-013-0007-5/}
}
TY  - JOUR
AU  - Li, Qin
AU  - Lin, Qun
AU  - Xie, Hehu
TI  - Nonconforming finite element approximations of the Steklov eigenvalue problem and its lower bound approximations
JO  - Applications of Mathematics
PY  - 2013
SP  - 129
EP  - 151
VL  - 58
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.1007/s10492-013-0007-5/
DO  - 10.1007/s10492-013-0007-5
LA  - en
ID  - 10_1007_s10492_013_0007_5
ER  - 
%0 Journal Article
%A Li, Qin
%A Lin, Qun
%A Xie, Hehu
%T Nonconforming finite element approximations of the Steklov eigenvalue problem and its lower bound approximations
%J Applications of Mathematics
%D 2013
%P 129-151
%V 58
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.1007/s10492-013-0007-5/
%R 10.1007/s10492-013-0007-5
%G en
%F 10_1007_s10492_013_0007_5
Li, Qin; Lin, Qun; Xie, Hehu. Nonconforming finite element approximations of the Steklov eigenvalue problem and its lower bound approximations. Applications of Mathematics, Tome 58 (2013) no. 2, pp. 129-151. doi: 10.1007/s10492-013-0007-5

Cité par Sources :