Interpolation error estimates for edge elements on anisotropic meshes
The classical error analysis for Nédélec edge interpolation requires the so-called regularity assumption on the elements. However, in Nicaise (2001, SIAM J. Numer. Anal., 39, 784-816) optimal error estimates were obtained for the lowest order case under the weaker hypothesis of the maximum angle con...
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2011
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| 100 | 1 | |a Lombardi, A.L. | |
| 245 | 1 | 0 | |a Interpolation error estimates for edge elements on anisotropic meshes |
| 260 | |c 2011 | ||
| 270 | 1 | 0 | |m Lombardi, A.L.; Instituto de Ciencias, Universidad Nacional de General Sarmiento, J.M. Gutierrez 1150, Los Polvorines, B1613GSX Provincia de Buenos Aires, Argentina; email: aldoc7@dm.uba.ar |
| 506 | |2 openaire |e Política editorial | ||
| 504 | |a Acosta, G., Apel, T., Duran, R.G., Lombardi, A.L., Anisotropic error estimates for an interpolant defined via moments (2008) Computing (Vienna/New York), 82 (1), pp. 1-9. , DOI 10.1007/s00607-008-0259-1 | ||
| 504 | |a Acosta, G., Apel, T., Durán, R.G., Lombardi, A.L., Error estimates for Raviart-Thomas interpolation of any order on anisotropic tetrahedra (2011) Math. Comput., 80, pp. 147-163 | ||
| 504 | |a Acosta, G., Durán, R.G., The maximum angle condition for mixed and nonconforming elements: Application to the Stokes equations (2000) SIAM J. Numer. Anal., 37, pp. 18-36 | ||
| 504 | |a Adams, R.A., (1975) Sobolev Spaces, , New York: Academic Press | ||
| 504 | |a Apel, T., (1999) Anisotropic Finite Elements: Local Estimates and Applications, , Stuttgart: Teubner | ||
| 504 | |a Babuska, I., Aziz, A.K., On the angle condition in the finite element method (1976) SIAM J. Numer. Anal., 13, pp. 214-226 | ||
| 504 | |a Brenner, S., Scott, L.R., (1994) The Mathematical Analysis of Finite Element Methods, , New York: Springer | ||
| 504 | |a Buffa, A., Costabel, M., Dauge, M., Algebraic convergence for anisotropic edge elements in polyhedral domains (2005) Numerische Mathematik, 101 (1), pp. 29-65. , DOI 10.1007/s00211-005-0607-4 | ||
| 504 | |a Caorsi, S., Fernandes, P., Raffetto, M., On the convergence of Galerkin finite element approximations of electromagnetic eigenproblems (2000) SIAM Journal on Numerical Analysis, 38 (2), pp. 580-607. , PII S0036142999357506 | ||
| 504 | |a Ciarlet, P., (1978) The Finite Element Method for Elliptic Problems., , Amsterdam: North Holland | ||
| 504 | |a Ciarlet, J.R.P., Zou, J., Fully discrete finite element approaches for time-dependent Maxwell's equations (1999) Numer. Math., 82, pp. 193-219 | ||
| 504 | |a Duppont, T., Scott, R., Polynomial approximation of functions in Sobolev spaces (1980) Math. Comput., 34, pp. 441-463 | ||
| 504 | |a Durán, R.G., Mixed finite element methods (1939) Mixed Finite Elements, Compatibility Conditions, and Applications, pp. 1-42. , (D. Boffi & L. Gastaldi eds). Lecture Notes in Mathematics Berlin: Springer | ||
| 504 | |a Girault, V., Raviart, P.A., (1986) Finite Element Methods for Navier-Stokes Equations. Theory and Applications, , Berlin: Springer | ||
| 504 | |a Jamet, P., Estimations d'erreur pour des éléments finis droits presque dégénérés (1976) RAIRO Anal. Numér, 10, pp. 46-71 | ||
| 504 | |a Krízek, M., On the maximum angle condition for linear tetrahedral elements (1992) SIAM J. Numer. Anal., 29, pp. 513-520 | ||
| 504 | |a Nédélec, J.C., Mixed finite elements in R3 (1980) Numer. Math., 35, pp. 315-341 | ||
| 504 | |a Nicaise, S., Edge elements on anisotropic meshes and approximation of the Maxwell equations (2001) SIAM J. Numer. Anal., 39, pp. 784-816 | ||
| 504 | |a Raviart, P.A., Thomas, J.-M., A mixed finite element method for second order elliptic problems (1977) Mathematical Aspects of the Finite Element Method, 606. , (I. Galligani & E. Magenes eds). Lectures Notes in Mathematics Berlin: Springer | ||
| 520 | 3 | |a The classical error analysis for Nédélec edge interpolation requires the so-called regularity assumption on the elements. However, in Nicaise (2001, SIAM J. Numer. Anal., 39, 784-816) optimal error estimates were obtained for the lowest order case under the weaker hypothesis of the maximum angle condition. This assumption allows for anisotropic meshes that become useful, for example, for the approximation of solutions with edge singularities. In this paper we prove optimal error estimates for the edge interpolation of any order under the maximum angle condition. We also obtain sharp stability results for that interpolation on appropriate families of elements. mixed finite elements; edge elements; anisotropic finite elements. © 2010 The author. |l eng | |
| 593 | |a Instituto de Ciencias, Universidad Nacional de General Sarmiento, J.M. Gutierrez 1150, Los Polvorines, B1613GSX Provincia de Buenos Aires, Argentina | ||
| 593 | |a Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, 1428 Buenos Aires, Argentina | ||
| 690 | 1 | 0 | |a ANISOTROPIC FINITE ELEMENTS |
| 690 | 1 | 0 | |a EDGE ELEMENTS |
| 690 | 1 | 0 | |a MIXED FINITE ELEMENTS |
| 773 | 0 | |d 2011 |g v. 31 |h pp. 1683-1712 |k n. 4 |p IMA J. Numer. Anal. |x 02724979 |w (AR-BaUEN)CENRE-1615 |t IMA Journal of Numerical Analysis | |
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