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Modeling dimensionally-heterogeneous problems: analysis, approximation and applications
journal contribution
posted on 2015-09-11, 14:11 authored by Pablo J. Blanco, Marco DiscacciatiMarco Discacciati, Alfio QuarteroniIn the present work a general theoretical framework for coupled dimensionally-heterogeneous partial differential equations is developed. This is done by recasting the variational formulation in terms of coupling interface variables. In such a general setting we analyze existence and uniqueness of solutions for both the continuous problem and its finite dimensional approximation. This approach also allows the development of different iterative substructuring solution methodologies involving dimensionally-homogeneous subproblems. Numerical experiments are carried out to test our theoretical results.
Funding
The first author acknowledges the support of the Brazilian agencies CNPq and FAPERJ. The second and third authors acknowledge the European Research Council Advanced Grant “Mathcard, Mathematical Modelling and Simulation of the Cardiovascular System”, Project ERC-2008-AdG 227058.
History
School
- Science
Department
- Mathematical Sciences
Published in
Numerische MathematikVolume
119Issue
2Pages
299 - 335Citation
BLANCO, P.J., DISCACCIATI, M. and QUARTERONI, A., 2011. Modeling dimensionally-heterogeneous problems: analysis, approximation and applications. Numerische Mathematik, 119 (2), pp. 299 - 335.Publisher
© Springer-VerlagVersion
- VoR (Version of Record)
Publisher statement
This work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/Publication date
2011Notes
This article is closed access.ISSN
0029-599XPublisher version
Language
- en