ETNA - Electronic Transactions on Numerical Analysis
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Verlag der Österreichischen Akademie der Wissenschaften Austrian Academy of Sciences Press
A-1011 Wien, Dr. Ignaz Seipel-Platz 2
Tel. +43-1-515 81/DW 3420, Fax +43-1-515 81/DW 3400 https://verlag.oeaw.ac.at, e-mail: verlag@oeaw.ac.at |
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DATUM, UNTERSCHRIFT / DATE, SIGNATURE
BANK AUSTRIA CREDITANSTALT, WIEN (IBAN AT04 1100 0006 2280 0100, BIC BKAUATWW), DEUTSCHE BANK MÜNCHEN (IBAN DE16 7007 0024 0238 8270 00, BIC DEUTDEDBMUC)
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ETNA - Electronic Transactions on Numerical Analysis ISBN 978-3-7001-8258-0 Online Edition Research Article
María González,
Hiram Varela
S. 706 - 725 doi:10.1553/etna_vol55s706 Verlag der Österreichischen Akademie der Wissenschaften doi:10.1553/etna_vol55s706
Abstract: In this paper we propose new adaptive stabilised mixed finite element methods for a nonlinear elliptic boundary value problem of second order in divergence form that appears, among other applications, in magnetostatics. The method is based on a three-field formulation that is augmented with suitable residual least-squares terms arising from the constitutive and equilibrium equations and from the equation that defines the gradient as an additional unknown. We show that the resulting scheme is well posed and obtain optimal error estimates. We also develop an a posteriori error analysis of residual type and derive a simple a posteriori error indicator which is reliable and locally efficient. Finally, we include several numerical experiments that confirm the theoretical results. Keywords: nonlinear boundary value problem, mixed finite element, stabilisation, a posteriori error estimates, magnetostatics Published Online: 2022/08/31 08:10:44 Object Identifier: 0xc1aa5576 0x003da7df Rights: . Electronic Transactions on Numerical Analysis (ETNA) is an electronic journal for the publication of significant new developments in numerical analysis and scientific computing. Papers of the highest quality that deal with the analysis of algorithms for the solution of continuous models and numerical linear algebra are appropriate for ETNA, as are papers of similar quality that discuss implementation and performance of such algorithms. New algorithms for current or new computer architectures are appropriate provided that they are numerically sound. However, the focus of the publication should be on the algorithm rather than on the architecture. The journal is published by the Kent State University Library in conjunction with the Institute of Computational Mathematics at Kent State University, and in cooperation with the Johann Radon Institute for Computational and Applied Mathematics of the Austrian Academy of Sciences (RICAM). Reviews of all ETNA papers appear in Mathematical Reviews and Zentralblatt für Mathematik. Reference information for ETNA papers also appears in the expanded Science Citation Index. ETNA is registered with the Library of Congress and has ISSN 1068-9613. …
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Verlag der Österreichischen Akademie der Wissenschaften Austrian Academy of Sciences Press
A-1011 Wien, Dr. Ignaz Seipel-Platz 2
Tel. +43-1-515 81/DW 3420, Fax +43-1-515 81/DW 3400 https://verlag.oeaw.ac.at, e-mail: verlag@oeaw.ac.at |