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Adaptive finite element methods for elliptic equations with non-smooth coefficients

Adaptive finite element methods for elliptic equations with non-smooth coefficients Numer. Math. (2000) 85: 579–608 Numerische Digital Object Identifier (DOI) 10.1007/s002110000135 Mathematik Adaptive finite element methods for elliptic equations with non-smooth coefficients 1 2 C. Bernardi ,R.Verfurth ¨ Analyse Numerique, ´ C.N.R.S. Universite ´ Pierre et Marie Curie, B.C. 187, 4 place Jussieu, F-75252 Paris Cedex 05, France; e-mail: [email protected] Fakultat ¨ fur ¨ Mathematik, Ruhr-Universitat ¨ Bochum, D-44780 Bochum, Germany; e-mail: [email protected] Received February 5, 1999 / Published online March 16, 2000 – Springer-Verlag 2000 Dedicated to Prof. P.-A. Raviart who showed us the beauty of Numerical Analysis Summary. We consider a second-order elliptic equation with discontinuous or anisotropic coefficients in a bounded two- or three dimensional domain, and its finite-element discretization. The aim of this paper is to prove some a priori and a posteriori error estimates in an appropriate norm, which are independent of the variation of the coefficients. Resum ´ e. ´ Nous considerons ´ une equation ´ elliptique du second ordre a ` co- efficients discontinus ou anisotropes dans un domaine borne ´ en dimension 2 ou 3, et sa discretisation ´ par el ´ ements ´ finis. Le but de cet article est de demontrer ´ des estimations d’erreur a priori et a http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Numerische Mathematik Springer Journals

Adaptive finite element methods for elliptic equations with non-smooth coefficients

Bernardi, C.; Verfürth, R.
Numerische Mathematik , Volume 85 (4) – Jun 1, 2000
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References (14)

Publisher
Springer Journals
Copyright
Copyright © 2000 by Springer-Verlag Berlin Heidelberg
Subject
Mathematics; Numerical Analysis; Mathematics, general; Theoretical, Mathematical and Computational Physics; Mathematical Methods in Physics; Numerical and Computational Physics, Simulation; Appl.Mathematics/Computational Methods of Engineering
ISSN
0029-599X
eISSN
0945-3245
DOI
10.1007/PL00005393
Publisher site
See Article on Publisher Site

Abstract

Numer. Math. (2000) 85: 579–608 Numerische Digital Object Identifier (DOI) 10.1007/s002110000135 Mathematik Adaptive finite element methods for elliptic equations with non-smooth coefficients 1 2 C. Bernardi ,R.Verfurth ¨ Analyse Numerique, ´ C.N.R.S. Universite ´ Pierre et Marie Curie, B.C. 187, 4 place Jussieu, F-75252 Paris Cedex 05, France; e-mail: [email protected] Fakultat ¨ fur ¨ Mathematik, Ruhr-Universitat ¨ Bochum, D-44780 Bochum, Germany; e-mail: [email protected] Received February 5, 1999 / Published online March 16, 2000 – Springer-Verlag 2000 Dedicated to Prof. P.-A. Raviart who showed us the beauty of Numerical Analysis Summary. We consider a second-order elliptic equation with discontinuous or anisotropic coefficients in a bounded two- or three dimensional domain, and its finite-element discretization. The aim of this paper is to prove some a priori and a posteriori error estimates in an appropriate norm, which are independent of the variation of the coefficients. Resum ´ e. ´ Nous considerons ´ une equation ´ elliptique du second ordre a ` co- efficients discontinus ou anisotropes dans un domaine borne ´ en dimension 2 ou 3, et sa discretisation ´ par el ´ ements ´ finis. Le but de cet article est de demontrer ´ des estimations d’erreur a priori et a

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Numerische Mathematik – Springer Journals

Published: Jun 1, 2000

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