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Modeling dimensionally-heterogeneous problems: analysis, approximation and applications
journal contributionposted 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.
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.
- Mathematical Sciences