Nonconforming finite element approximations of the Steklov eigenvalue problem

Authors:
Yidu Yang;Qin Li;Sirui Li
Affiliations:
School of Mathematics and Computer Science, Guizhou Normal University, GuiYang, 550001, China;School of Mathematics and Computer Science, Guizhou Normal University, GuiYang, 550001, China;School of Mathematics and Computer Science, Guizhou Normal University, GuiYang, 550001, China
Venue:
Applied Numerical Mathematics
Year:
2009

Citing 3
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Abstract

This paper deals with nonconforming finite element approximations of the Steklov eigenvalue problem. For a class of nonconforming finite elements, it is shown that the j-th approximate eigenpair converges to the j-th exact eigenpair and error estimates for eigenvalues and eigenfunctions are derived. Furthermore, it is proved that the j-th eigenvalue derived by the EQ"1^r^o^t element gives lower bound of the j-th exact eigenvalue, whereas the nonconforming Crouzeix-Raviart element and the Q"1^r^o^t element provide lower bounds of the large eigenvalues. Numerical results are presented to confirm the considered theory.