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Defective Boundary Conditions for PDEs with Applications in Haemodynamics

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Numerical Methods for PDEs

Part of the book series: SEMA SIMAI Springer Series ((SEMA SIMAI,volume 15))

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Abstract

This works gives an overview of the mathematical treatment of state-of-the-art techniques for partial differential problems where boundary data are provided only in terms of averaged quantities. A condition normally indicated as “defective boundary condition”. We present and analyze several procedures by which this type of problems can be handled.

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Acknowledgements

The authors would like to thank B. Guerciotti and D. Le Van for their support in the numerical experiments, and dr M. Domanin for providing the radiological images. They also gratefully acknowledge the financial support of the Italian MIUR by the grant PRIN12, number 201289A4LX, “Mathematical and numerical models of the cardiovascular system, and their clinical applications”. CV has been partially supported also by the H2020-MSCA-ITN-2017, EU project 765374 “ROMSOC - Reduced Order Modelling, Simulation and Optimization of Coupled systems”.

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Authors and Affiliations

  1. MOX, Dipartimento di Matematica, Politecnico di Milano, Milano, Italy

    Luca Formaggia & Christian Vergara

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  1. Luca Formaggia
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  2. Christian Vergara
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Correspondence to Luca Formaggia .

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Editors and Affiliations

  1. Institut Montpelliérain Alexander Grothendieck, CNRS, Université Montpellier, Montpellier, France

    Daniele Antonio Di Pietro

  2. Universit Paris Est, CERMICS (ENPC), Marne la Vallée, France

    Alexandre Ern

  3. MOX - Dipartimento di Matematica, Politecnico di Milano, Milano, Italy

    Luca Formaggia

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Formaggia, L., Vergara, C. (2018). Defective Boundary Conditions for PDEs with Applications in Haemodynamics. In: Di Pietro, D., Ern, A., Formaggia, L. (eds) Numerical Methods for PDEs. SEMA SIMAI Springer Series, vol 15. Springer, Cham. https://doi.org/10.1007/978-3-319-94676-4_10

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