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.

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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 
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     title = {Nonconforming finite element approximations of the {Steklov} eigenvalue problem and its lower bound approximations},
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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. http://geodesic.mathdoc.fr/articles/10.1007/s10492-013-0007-5/

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