Armentano, María G. The effect of reduced integration in the Steklov eigenvalue problem. (English) Zbl 1077.65115 M2AN, Math. Model. Numer. Anal. 38, No. 1, 27-36 (2004). The author studies the effect of introducing a numerical integration in the piecewise linear finite element approximation of the Steklov eigenvalue problem. As a consequence the author obtains optimal order error estimates for the eigenfunctions. Some results concerning the singular eigenfunctions are also obtained. Reviewer: Răzvan Răducanu (Iaşi) Cited in 17 Documents MSC: 65N25 Numerical methods for eigenvalue problems for boundary value problems involving PDEs 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs 35P15 Estimates of eigenvalues in context of PDEs 65N15 Error bounds for boundary value problems involving PDEs Keywords:finite element; eigenfunctions; eigenvalues; Steklov eigenvalue problem; error estimates PDF BibTeX XML Cite \textit{M. G. Armentano}, M2AN, Math. Model. Numer. Anal. 38, No. 1, 27--36 (2004; Zbl 1077.65115) Full Text: DOI Numdam EuDML OpenURL References: [1] M.G. Armentano and R.G. Durán , Mass lumping or not mass lumping for eigenvalue problems . Numer. Methods Partial Differential Equations 19 ( 2003 ) 653 - 664 . Zbl 1041.65086 · Zbl 1041.65086 [2] I. Babuska and J. Osborn , Eigenvalue Problems , Handbook of Numerical Analysis, Vol. II. Finite Element Methods (Part. 1) ( 1991 ). MR 1115240 | Zbl 0875.65087 · Zbl 0875.65087 [3] U. Banerjee and J. Osborn , Estimation of the effect of numerical integration in finite element eigenvalue approximation . Numer. Math. 56 ( 1990 ) 735 - 762 . Article | Zbl 0693.65071 · Zbl 0693.65071 [4] F.B. Belgacem and S.C. Brenner , Some nonstandard finite element estimates with applications to 3D Poisson and Signorini problems . Electron. Trans. Numer. Anal. 12 ( 2001 ) 134 - 148 . Zbl 0981.65131 · Zbl 0981.65131 [5] A. Bermudez , R. Rodriguez and D. Santamarina , A finite element solution of an added mass formulation for coupled fluid-solid vibrations . Numer. Math. 87 ( 2000 ) 201 - 227 . Zbl 0998.76046 · Zbl 0998.76046 [6] S.C. Brenner and L.R. Scott , The Mathematical Theory of Finite Element Methods . Springer-Verlag, New York ( 1994 ). MR 1278258 | Zbl 0804.65101 · Zbl 0804.65101 [7] P. Ciarlet , The Finite Element Method for Elliptic Problems . North-Holland, Amsterdam ( 1978 ). MR 520174 | Zbl 0383.65058 · Zbl 0383.65058 [8] P. Grisvard , Elliptic Problems in Nonsmooth Domain . Pitman Boston ( 1985 ). MR 775683 | Zbl 0695.35060 · Zbl 0695.35060 [9] H.J.-P. Morand and R. Ohayon , Interactions Fluids-Structures . Rech. Math. Appl. 23 ( 1985 ). · Zbl 0754.73071 [10] H.F. Weinberger , Variational Methods for Eigenvalue Approximation . SIAM, Philadelphia ( 1974 ). MR 400004 | Zbl 0296.49033 · Zbl 0296.49033 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.