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Computational modelling of multiscale, multiphase fluid mixtures with application to tumour growth

Collis, Joe; Hubbard, Matthew E.; O'Dea, Reuben D.

Authors

Joe Collis Joe.Collis@nottingham.ac.uk

MATTHEW HUBBARD MATTHEW.HUBBARD@NOTTINGHAM.AC.UK
Professor of Computational and Applied Mathematics



Abstract

In this work we consider the discretization of a recently formulated (Collis et al., [22]) multiscale model for drug- and nutrient-limited tumour growth. The key contribution of this work is the proposal of a discontinuous Galerkin finite element scheme which incorporates a non-standard coupling across a singular surface, and the presentation of full details of a suitable discretization for the coupled flow and transport systems, such as that arising in Collis et al. [22] and other similar works. We demonstrate the application of the proposed discretizations via representative numerical experiments; furthermore, we present a short numerical study of convergence for the proposed microscale scheme, in which we observe optimal rates of convergence for sufficiently smooth data.

Citation

Collis, J., Hubbard, M. E., & O'Dea, R. D. (2016). Computational modelling of multiscale, multiphase fluid mixtures with application to tumour growth. Computer Methods in Applied Mechanics and Engineering, 309, https://doi.org/10.1016/j.cma.2016.06.015

Journal Article Type Article
Acceptance Date Jun 11, 2016
Online Publication Date Jun 21, 2016
Publication Date Sep 1, 2016
Deposit Date Jul 19, 2016
Publicly Available Date Jul 19, 2016
Journal Computer Methods in Applied Mechanics and Engineering
Print ISSN 0045-7825
Electronic ISSN 1879-2138
Publisher Elsevier
Peer Reviewed Peer Reviewed
Volume 309
DOI https://doi.org/10.1016/j.cma.2016.06.015
Keywords Numerical simulations; Finite elements; Porous media; Cancer modelling
Public URL http://eprints.nottingham.ac.uk/id/eprint/35156
Publisher URL http://www.sciencedirect.com/science/article/pii/S0045782516305746
Copyright Statement Copyright information regarding this work can be found at the following address: http://creativecommons.org/licenses/by-nc-nd/4.0

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Copyright Statement
Copyright information regarding this work can be found at the following address: http://creativecommons.org/licenses/by-nc-nd/4.0





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