A posteriori error estimates for the Steklov eigenvalue problem

In this paper we introduce and analyze an a posteriori error estimator for the linear finite element approximations of the Steklov eigenvalue problem. We define an error estimator of the residual type which can be computed locally from the approximate eigenpair and we prove that, up to higher order...

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Autor principal: Armentano, M.G
Otros Autores: Padra, C.
Formato: Capítulo de libro
Lenguaje:Inglés
Publicado: 2008
Acceso en línea:Registro en Scopus
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100 1 |a Armentano, M.G. 
245 1 2 |a A posteriori error estimates for the Steklov eigenvalue problem 
260 |c 2008 
270 1 0 |m Armentano, M.G.; Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, 1428 Buenos Aires, Argentina; email: garmenta@dm.uba.ar 
506 |2 openaire  |e Política editorial 
504 |a Andreev, A.B., Hristov, A.H., On the variational aspects for elliptic problems with parameter on the boundary (1999) Recent Advances in Numerical Methods and Applications II, Proceedings of the Fourth International Conference, pp. 587-593. , Sofia, Bulgaria, 1998, World Scientific, River Edge, NJ 
504 |a Andreev, A.B., Todorov, T.D., Isoparametric finite-element approximation of a Steklov eigenvalue problem (2004) IMA J. Numer. Anal., 24, pp. 309-322 
504 |a Ainsworth, M., Oden, J.T., (2000) A Posteriori Error Estimation in Finite Element Analysis, , Wiley, New York 
504 |a Armentano, M.G., The effect of reduced integration in the Steklov eigenvalue problem (2004) Math. Mod. Numer. Anal. (M2AN), 38 (1), pp. 27-36 
504 |a Babuška, I., Miller, A., A feedback finite element method with a posteriori error estimation. Part I: The finite element method and some basic properties of the a posteriori error estimator (1987) Comp. Meth. Appl. Mech. Engrg., 61, pp. 1-40 
504 |a Babuška, I., Osborn, J., Eigenvalue problems (1991) Handbook of Numerical Analysis, II, pp. 640-787. , Finite Element Methods (Part 1). Ciarlet P.G., and Lions J.L. (Eds), Elsevier (North-Holland), Amsterdam 
504 |a Bergmann, S., Schiffer, M., (1953) Kernel Functions and Elliptic Differential Equations in Mathematical Physics, , Academic Press, New York 
504 |a Bermúdez, A., Durán, R., Rodríguez, R., Finite element solution of incompressible fluid-structure vibration problems (1997) Internat. J. Numer. Meth. Eng., 40, pp. 1435-1448 
504 |a Bermúdez, A., Rodríguez, R., Santamarina, D., A finite element solution of an added mass formulation for coupled fluid-solid vibrations (2000) Numer. Math., 87, pp. 201-227 
504 |a Carstensen, C., Verfürth, R., Edge residuals dominate a posteriori error estimates for low order finite element methods (1999) SIAM J. Numer. Anal., 36, pp. 1571-1587 
504 |a Ciarlet, P., (1978) The Finite Element Method for Elliptic Problems, , North-Holland, Amsterdam 
504 |a Conca, C., Planchard, J., Vanninathan, M., (1995) Fluid and Periodic Structures, , John Wiley & Sons, New York 
504 |a Durán, R.G., Padra, C., Rodríguez, R., A posteriori error estimates for the finite element approximation of eigenvalue problems (2003) Math. Mod. & Met. Appl. Sci. (M3AS), 13 (8), pp. 1219-1229 
504 |a Durán, R.G., Gastaldi, L., Padra, C., A posteriori error estimators for mixed approximations of eigenvalue problems (1999) Math. Mod. & Met. Appl. Sci. (M3AS), 9 (8), pp. 1165-1178 
504 |a Grisvard, P., (1985) Elliptic Problems in Nonsmooth Domain, , Pitman, Boston 
504 |a Larson, M.G., A posteriori and a priori error analysis for finite elements approximations of self-adjoint elliptic eigenvalue problems (2000) SIAM J. Numer. Anal., 38, pp. 608-625 
504 |a Morand, H.J.P., Ohayon, R., (1995) Fluid-Structure Interaction: Applied Numerical Methods, , John Wiley & Sons, New York 
504 |a Nochetto, R., Pointwise a posteriori error estimates for elliptic problems on highly graded meshes (1995) Math. Comp., 64, pp. 1-22 
504 |a Rodríguez, R., Some remarks on Zienkiewicz-Zhu estimator (1994) Numer. Meth. PDE, 10, pp. 625-635 
504 |a Verfürth, R., (1996) A Review of A Posteriori Error Estimation and Adaptive Mesh-Refinement Techniques, , Wiley & Teubner, New York 
504 |a Verfürth, R., A posteriori error estimates for nonlinear problems (1989) Math. Comp., 62, pp. 445-475 
504 |a Weinberger, H.F., (1974) Variational Methods for Eigenvalue Approximation, , SIAM, Philadelphia, PA 
520 3 |a In this paper we introduce and analyze an a posteriori error estimator for the linear finite element approximations of the Steklov eigenvalue problem. We define an error estimator of the residual type which can be computed locally from the approximate eigenpair and we prove that, up to higher order terms, the estimator is equivalent to the energy norm of the error. Finally, we prove that the volumetric part of the residual term is dominated by a constant times the edge residuals, again up to higher order terms. © 2007 IMACS.  |l eng 
536 |a Detalles de la financiación: Fundación Antorchas 
536 |a Detalles de la financiación: Agencia Nacional de Promoción Científica y Tecnológica, PICT 03-05009 
536 |a Detalles de la financiación: Supported by ANPCyT under grant PICT 03-05009 and Fundación Antorchas. The authors are members of CONICET, Argentina. Corresponding author. E-mail addresses: garmenta@dm.uba.ar (M.G. Armentano), padra@cab.cnea.gov.ar (C. Padra). 
593 |a Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, 1428 Buenos Aires, Argentina 
593 |a Centro Atómico Bariloche, 4800 Bariloche, Argentina 
690 1 0 |a A POSTERIORI ERROR ESTIMATES 
690 1 0 |a FINITE ELEMENTS 
690 1 0 |a STEKLOV EIGENVALUE PROBLEM 
690 1 0 |a ERROR ANALYSIS 
690 1 0 |a FINITE ELEMENT METHOD 
690 1 0 |a PROBLEM SOLVING 
690 1 0 |a POSTERIORI ERROR ESTIMATES 
690 1 0 |a STEKLOV EIGENVALUE PROBLEM 
690 1 0 |a EIGENVALUES AND EIGENFUNCTIONS 
700 1 |a Padra, C. 
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