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Modeling dimensionally-heterogeneous problems: analysis, approximation and applications

journal contribution
posted on 11.09.2015, 14:11 by Pablo J. Blanco, Marco DiscacciatiMarco Discacciati, Alfio Quarteroni
In 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 Mathematik

Volume

119

Issue

2

Pages

299 - 335

Citation

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-Verlag

Version

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

2011

Notes

This article is closed access.

ISSN

0029-599X

Language

en

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