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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Elsevier B.V.
2017
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| 003 | AR-BaUEN | ||
| 005 | 20230518204533.0 | ||
| 008 | 190410s2017 xx ||||fo|||| 00| 0 eng|d | ||
| 024 | 7 | |2 scopus |a 2-s2.0-85007256434 | |
| 040 | |a Scopus |b spa |c AR-BaUEN |d AR-BaUEN | ||
| 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 | |
| 856 | 4 | 1 | |u https://www.scopus.com/inward/record.uri?eid=2-s2.0-85007256434&doi=10.1016%2fj.cam.2016.11.041&partnerID=40&md5=fe441d7a919889fde5566873c6422fd7 |y Registro en Scopus |
| 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 |
| 856 | 4 | 0 | |u https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03770427_v317_n_p218_Acosta |y Registro en la Biblioteca Digital |
| 961 | |a paper_03770427_v317_n_p218_Acosta |b paper |c PE | ||
| 962 | |a info:eu-repo/semantics/article |a info:ar-repo/semantics/artículo |b info:eu-repo/semantics/publishedVersion | ||
| 999 | |c 75902 | ||