The minimal angle condition for quadrilateral finite elements of arbitrary degree

We study W1,p Lagrange interpolation error estimates for general quadrilateral Qk finite elements with k≥2. For the most standard case of p=2 it turns out that the constant C involved in the error estimate can be bounded in terms of the minimal interior angle of the quadrilateral. Moreover, the same...

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Autor principal: Acosta, G.
Otros Autores: Monzón, G.
Formato: Capítulo de libro
Lenguaje:Inglés
Publicado: Elsevier B.V. 2017
Acceso en línea:Registro en Scopus
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100 1 |a Acosta, G. 
245 1 4 |a The minimal angle condition for quadrilateral finite elements of arbitrary degree 
260 |b Elsevier B.V.  |c 2017 
270 1 0 |m Acosta, G.; Universidad de Buenos Aires, IMAS-CONICET, Departamento de Matematica, Pabellón I Facultad de Ciencias Exactas y NaturalesArgentina; email: gacosta@dm.uba.ar 
506 |2 openaire  |e Política editorial 
504 |a Ciarlet, P.G., Raviart, P.A., Interpolation theory over curved elements, with applications to finite elements methods (1972) Comput. Methods Appl. Mech. Engrg., 1, pp. 217-249 
504 |a Babuška, I., Aziz, A.K., On the angle condition in the finite element method (1976) SIAM J. Numer. Anal., 13, pp. 214-226 
504 |a Jamet, P., Estimations d'erreur pour des éléments finis droits presque degénérés (1976) RAIRO Anal. Numer., 10, pp. 46-61 
504 |a Jamet, P., Estimation of the interpolation error for quadrilateral finite elements which can degenerate into triangles (1977) SIAM J. Numer. Anal., 14, pp. 925-930 
504 |a Zenisek, A., Vanmaele, M., The interpolation theorem for narrow quadrilateral isoparametric finite elements (1995) Numer. Math., 72, pp. 123-141 
504 |a Zenisek, A., Vanmaele, M., Applicability of the Bramble Hilbert lemma in interpolation problems of narrow quadrilateral isoparametric finite elements (1995) J. Comput. Appl. Math., 63, pp. 109-122 
504 |a Apel, T., Anisotropic interpolation error estimates for isoparametric quadrilateral finite elements (1998) Computing, 60, pp. 157-174 
504 |a Apel, T., (1999) : Anisotropic Finite Elements: Local Estimates and Applications, Advances in Numerical Mathematics, , B. G. Teubner Stuttgart, Leipzig 
504 |a Acosta, G., Durán, R.G., Error estimates for Q1 isoparametric elements satisfying a weak angle condition (2000) SIAM J. Numer. Anal., 38, pp. 1073-1088 
504 |a Acosta, G., Monzón, G., Interpolation error estimates in W1,p for degenerate Q1 isoparametric elements (2006) Numer. Math., 104, pp. 129-150 
504 |a Mao, S., Nicaise, S., Shi, Z.C., On the interpolation error estimates for Q1 quadrilateral finite elements (2008) SIAM J. Numer. Anal., 47, pp. 467-486 
504 |a Acosta, G., Durán, R.G., The maximum angle condition for mixed and nonconforming elements: Application to the Stokes equations (1999) SIAM J. Numer. Anal., 37, pp. 18-36 
504 |a Verfhürt, R., Error estimates for some quasi-interpolation operators (1999) RAIRO Math. Model. Numer. Anal., 33 (4), pp. 695-713 
504 |a Arnold, D.N., Boffi, D., Falk, R.S., Approximation by quadrilateral finite elements (2002) Math. Comp., 71, p. 239. , 909–922 
520 3 |a We study W1,p Lagrange interpolation error estimates for general quadrilateral Qk finite elements with k≥2. For the most standard case of p=2 it turns out that the constant C involved in the error estimate can be bounded in terms of the minimal interior angle of the quadrilateral. Moreover, the same holds for any p in the range 1≤p<3. On the other hand, for 3≤p we show that C also depends on the maximal interior angle. We provide some counterexamples showing that our results are sharp. © 2016 Elsevier B.V.  |l eng 
593 |a Universidad de Buenos Aires, IMAS-CONICET, Departamento de Matematica, Pabellón I Facultad de Ciencias Exactas y Naturales, Buenos Aires, 1428, Argentina 
593 |a Instituto de Ciencias, Universidad Nacional de General Sarmiento, J.M. Gutiérrez 1150, (1613) Los Polvorines, Buenos Aires, Argentina 
690 1 0 |a ANISOTROPIC FINITE ELEMENTS 
690 1 0 |a LAGRANGE INTERPOLATION 
690 1 0 |a MAXIMUM ANGLE CONDITION 
690 1 0 |a MINIMUM ANGLE CONDITION 
690 1 0 |a QUADRILATERAL ELEMENTS 
690 1 0 |a INTERPOLATION 
690 1 0 |a ANISOTROPIC FINITE ELEMENTS 
690 1 0 |a LAGRANGE INTERPOLATIONS 
690 1 0 |a MAXIMUM ANGLE CONDITION 
690 1 0 |a MINIMUM ANGLE CONDITION 
690 1 0 |a QUADRILATERAL ELEMENTS 
690 1 0 |a LAGRANGE MULTIPLIERS 
700 1 |a Monzón, G. 
773 0 |d Elsevier B.V., 2017  |g v. 317  |h pp. 218-234  |p J. Comput. Appl. Math.  |x 03770427  |w (AR-BaUEN)CENRE-1107  |t Journal of Computational and Applied Mathematics 
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856 4 0 |u https://doi.org/10.1016/j.cam.2016.11.041  |y DOI 
856 4 0 |u https://hdl.handle.net/20.500.12110/paper_03770427_v317_n_p218_Acosta  |y Handle 
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