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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| Formato: | Capítulo de libro |
| Lenguaje: | Inglés |
| Publicado: |
Elsevier B.V.
2017
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| Acceso en línea: | Registro en Scopus DOI Handle Registro en la Biblioteca Digital |
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| Sumario: | 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. |
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| Bibliografía: | 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 Babuška, I., Aziz, A.K., On the angle condition in the finite element method (1976) SIAM J. Numer. Anal., 13, pp. 214-226 Jamet, P., Estimations d'erreur pour des éléments finis droits presque degénérés (1976) RAIRO Anal. Numer., 10, pp. 46-61 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 Zenisek, A., Vanmaele, M., The interpolation theorem for narrow quadrilateral isoparametric finite elements (1995) Numer. Math., 72, pp. 123-141 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 Apel, T., Anisotropic interpolation error estimates for isoparametric quadrilateral finite elements (1998) Computing, 60, pp. 157-174 Apel, T., (1999) : Anisotropic Finite Elements: Local Estimates and Applications, Advances in Numerical Mathematics, , B. G. Teubner Stuttgart, Leipzig 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 Acosta, G., Monzón, G., Interpolation error estimates in W1,p for degenerate Q1 isoparametric elements (2006) Numer. Math., 104, pp. 129-150 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 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 Verfhürt, R., Error estimates for some quasi-interpolation operators (1999) RAIRO Math. Model. Numer. Anal., 33 (4), pp. 695-713 Arnold, D.N., Boffi, D., Falk, R.S., Approximation by quadrilateral finite elements (2002) Math. Comp., 71, p. 239. , 909–922 |
| ISSN: | 03770427 |
| DOI: | 10.1016/j.cam.2016.11.041 |