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myref.bib
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@article{Eymard2010,
author = {Eymard, R. and Gallou{\"{e}}t, T. and Herbin, R.},
journal = {IMA Journal of Numerical Analysis},
keywords = {finite-volume schemes,heterogeneous anisotropic diffusion,nonconforming grids},
number = {4},
pages = {1009--1043},
title = {{Discretization of heterogeneous and anisotropic diffusion problems on general nonconforming meshes}},
volume = {30},
year = {2010}
}
@article{renard2009,
title={A new fictitious domain approach inspired by the extended finite element method},
author={Haslinger, Jaroslav and Renard, Yves},
journal={SIAM Journal on Numerical Analysis},
volume={47},
number={2},
pages={1474--1499},
year={2009},
publisher={SIAM}
}
@article{cumsille2014,
title={A novel model for biofilm growth and its resolution by using the hybrid immersed interface-level set method},
author={Cumsille, Patricio and Asenjo, Juan A and Conca, Carlos},
journal={Computers \& Mathematics with Applications},
volume={67},
number={1},
pages={34--51},
year={2014},
publisher={Elsevier}
}
@article{zhang2017,
title={Modeling of Biofilm Growth on Ager Substrate Using the Extended Finite Element Method},
author={Zhang, Xianlong and Wang, Xiaoling and Sun, Qingping},
journal={Procedia IUTAM},
volume={23},
pages={33--41},
year={2017},
publisher={Elsevier}
}
@article{renard2016,
title={A fictitious domain method for frictionless contact problems in elasticity using Nitsche's method},
author={Fabre, Mathieu and Pousin, J{\'e}r{\^o}me and Renard, Yves},
journal={SMAI Journal of Computational Mathematics},
volume={2},
pages={19--50},
year={2016}
}
@article{barbosa1991,
title={The finite element method with Lagrange multipliers on the boundary: circumventing the Babu{\v{s}}ka-Brezzi condition},
author={Barbosa, Helio JC and Hughes, Thomas JR},
journal={Computer Methods in Applied Mechanics and Engineering},
volume={85},
number={1},
pages={109--128},
year={1991},
publisher={Elsevier}
}
@article{Frey2012,
title={Computation of the signed distance function to a discrete contour on adapted triangulation},
author={Dapogny, Charles and Frey, Pascal},
journal={Calcolo},
volume={49},
number={3},
pages={193--219},
year={2012},
publisher={Springer}
}
@book{quarteroni1994,
title={Numerical Approximation of Partial Differential Equations},
author={Quarteroni, Alfio and Valli, Alberto},
year={1994},
publisher={Springer}
}
@book{osher2006book,
title={Level set methods and dynamic implicit surfaces},
author={Osher, Stanley and Fedkiw, Ronald},
volume={153},
year={2006},
publisher={Springer Science \& Business Media}
}
@article{chen1995,
title={Lattice methods and their applications to reacting systems},
author={Chen, Shiyi and Dawson, SP and Doolen, GD and Janecky, DR and Lawniczak, A},
journal={Computers \& chemical engineering},
volume={19},
number={6-7},
pages={617--646},
year={1995},
publisher={Elsevier}
}
@article{Eymard2008,
title={Discretization schemes for heterogeneous and anisotropic diffusion problems on general nonconforming meshes},
author={Eymard, Robert and Gallou{\"e}t, Thierry and Herbin, Raphaele},
journal={Available online as HAL report},
volume={203269},
year={2008}
}
@article{DiPietro2010,
author = {{Di Pietro}, Daniele A. and Ern, Alexandre},
doi = {10.1090/S0025-5718-10-02333-1},
issn = {0025-5718},
journal = {Mathematics of Computation},
number = {271},
pages = {1303--1330},
title = {{Discrete functional analysis tools for Discontinuous Galerkin methods with application to the incompressible Navier–Stokes equations}},
url = {http://www.scopus.com/inward/record.url?eid=2-s2.0-77956573267{\&}partnerID=tZOtx3y1},
volume = {79},
year = {2010}
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@book{Ainsworth1997,
author = {Ainsworth, Mark and Oden, J.Tinsley T},
booktitle = {Computer Methods in Applied Mechanics and Engineering},
doi = {10.1016/S0045-7825(96)01107-3},
editor = {{Myron B. Allen III, David A. Cox}, Peter Lax},
file = {:Users/dinhanhthi/Dropbox/PhD/docs/fem{\_}methods/uniqueness existence nonlinear system/a posteriori error fem - Mark Ainsworth - Tinsley Oden BOOK.pdf:pdf},
isbn = {047129411X},
issn = {00457825},
publisher = {John Wiley and Sons},
title = {{A posteriori error estimation in finite element analysis}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S0045782596011073},
year = {1997}
}
@book{Debnath2005,
author = {Debnath, L and Mikusi{\'{n}}ski, P},
file = {:Users/dinhanhthi/Dropbox/PhD/docs/back{\_}ground/analysis/hilbert spaces with applications - Debnath - Mikusinski.pdf:pdf},
isbn = {9780122084386},
title = {{Hilbert spaces with applications}},
year = {2005}
}
@book{Leoni2009,
author = {Leoni, Giovanni},
file = {:Users/dinhanhthi/Library/Application Support/Mendeley Desktop/Downloaded/Leoni - 2009 - A first course in Sobolev spaces.pdf:pdf},
isbn = {9780821847688},
mendeley-groups = {background},
publisher = {American Mathematical Society},
title = {{A first course in Sobolev spaces}},
volume = {105},
year = {2009}
}
@article{Baratchart2016,
archivePrefix = {arXiv},
arxivId = {arXiv:1412.3283v1},
author = {Baratchart, Laurent and Bourgeois, Laurent and Leblond, Juliette},
doi = {10.1016/j.jfa.2016.01.011},
eprint = {arXiv:1412.3283v1},
file = {:Users/dinhanhthi/Dropbox/PhD/docs/back{\_}ground/analysis/robin laplace exist unique.pdf:pdf},
issn = {10960783},
journal = {Journal of Functional Analysis},
keywords = {Elliptic regularity,Holomorphic Hardy-Smirnov classes,Robin inverse problem,Unique continuation},
number = {7},
pages = {2508--2542},
title = {{Uniqueness results for inverse Robin problems with bounded coefficient}},
volume = {270},
year = {2016}
}
@article{Duddu2006,
author = {Duddu, Ravindra and Bordas, S and Moran, Brian and Chopp, David L},
journal = {International journal for numerical method in engineering int.},
keywords = {Biofilm,Level set,Velocity extension,XFEM},
language = {english},
number = {847},
pages = {1--33},
title = {{A combined extended finite element and level set method for biofilm growth}},
volume = {2},
year = {2006}
}
@book{Rittmann2001,
author = {Rittmann, Bruce E. and McCarty, Perry L.},
file = {:C$\backslash$:/Users/dinha/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/B.E, McCarty - 2001 - Environmental Biotechnology.pdf:pdf},
isbn = {0-07-118184-9},
mendeley-groups = {level set method},
publisher = {Mc Graw Hill},
title = {{Environmental Biotechnology: principles and applications}},
year = {2001}
}
@book{Walker2008,
author = {Walker, V. K. and Wilson, S. L. and Wu, Z. and Miao, D. N. and Zeng, H. and Ripmeester, J. A. and Palmer, G. R.},
booktitle = {Emerging Environmental Technologies},
doi = {10.1007/978-1-4020-8786-8},
file = {:C$\backslash$:/Users/dinha/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/Walker et al. - 2008 - Emerging Environmental Technologies.pdf:pdf},
isbn = {978-1-4020-8785-1},
keywords = {Gas hydrates,antifreeze proteins,freeze-thaw,gas exploration,ice affinity,ice nucleators,overwintering},
pages = {29--41},
title = {{Emerging Environmental Technologies}},
url = {http://www.scopus.com/inward/record.url?eid=2-s2.0-68149172274{\&}partnerID=tZOtx3y1},
year = {2008}
}
@article{Duddu2008,
author = {Duddu, Ravindra and Chopp, David L and Moran, Brian},
doi = {10.1002/bit.22233},
institution = {Department of Civil and Environmental Engineering, Northwestern University, 2145 Sheridan Rd, Evanston, Illinois 60208, USA. [email protected]},
issn = {1097-0290},
journaltitle = {Biotechnology and bioengineering},
month = may,
number = {1},
pages = {92--104},
pmid = {19213021},
title = {{A two-dimensional continuum model of biofilm growth incorporating fluid flow and shear stress based detachment.}},
volume = {103},
year = {2008}
}
@article{Mah2001,
author = {Mah, Thien-Fah C. and O'Toole, George A.},
issn = {0966-842X},
journal = {Trends in microbiology},
month = jan,
number = {1},
pages = {34--9},
pmid = {11166241},
title = {{Mechanisms of biofilm resistance to antimicrobial agents}},
volume = {9},
year = {2001}
}
@article{Chopp2002,
author = {Chopp, David L and Kirisits, M J and Moran, Brian and Parsek, M R},
doi = {10.1038/sj.jim.7000316},
issn = {1367-5435},
journal = {Journal of industrial microbiology \& biotechnology},
mendeley-groups = {biofilm,papers},
month = dec,
number = {6},
pages = {339--46},
pmid = {12483476},
title = {{A mathematical model of quorum sensing in a growing bacterial biofilm.}},
volume = {29},
year = {2002}
}
@book{Thomee2006,
author = {Thom\'{e}e, Vidar},
edition = {2},
editor = {Bank, R. and Graham, R.L. and Stoer, J. and Varga, R. and Yserentant, H.},
isbn = {978-3-540-33122-3},
keywords = {Galerkin methods,differential equations,finite element theory,parabolic partial},
pages = {370},
publisher = {Springer},
series = {Springer Series in Computational Mathematics},
title = {{Galerkin Finite Element Methods for Parabolic Problems}},
volume = {25},
year = {2006}
}
@book{Knabner2002,
address = {New York},
author = {Knabner, Peter and Angermann, Lutz},
editor = {Marsden, J.E. and Sirovich, L. and Antman, S.S.},
isbn = {038795449X},
keywords = {numerical method},
pages = {442},
publisher = {Springer},
series = {Texts in Applied Mathematics},
title = {{Numerical Methods for Elliptic and Parabolic Partial Differential Equations}},
year = {2002}
}
@article{Picioreanu2000,
author = {Picioreanu, Cristian and {Van Loosdrecht}, M C and Heijnen, J J},
issn = {0006-3592},
journal = {Biotechnology and bioengineering},
keywords = {Algorithms,Biofilms,Biological,Biotechnology,Biotechnology: methods,Diffusion,Models,Surface Properties},
month = sep,
number = {5},
pages = {504--15},
pmid = {10898860},
title = {{Effect of diffusive and convective substrate transport on biofilm structure formation: a two-dimensional modeling study.}},
volume = {69},
year = {2000}
}
@book{picioreanuThesis,
title={Multidimensional modeling of biofilm structure},
author={Picioreanu, Cristian and van Loosdrecht, M and Heijnen, J},
year={1999},
publisher={Delft University of Technology, Faculty of Applied Sciences}
}
@article{Rittma1982,
author = {Rittman, B E},
doi = {10.1002/bit.260240219},
issn = {0006-3592},
journal = {Biotechnology and bioengineering},
number = {2},
pages = {501--506},
pmid = {18546318},
title = {{The Effect of Shear Stress on Bioflm Loss Rate}},
volume = {24},
year = {1982}
}
@article{monod1949,
author = { Jacques Monod },
title = {The Growth of Bacterial Cultures},
journal = {Annual Review of Microbiology},
volume = {3},
number = {1},
pages = {371-394},
year = {1949},
doi = {10.1146/annurev.mi.03.100149.002103}
}
@article{picioreanu2001,
title={Two-dimensional model of biofilm detachment caused by internal stress from liquid flow},
author={Picioreanu, Cristian and Van Loosdrecht, Mark CM and Heijnen, Joseph J and others},
journal={Biotechnology \& Bioengineering},
volume={72},
number={2},
pages={205--218},
year={2001},
publisher={Citeseer}
}
@article{cogan2007,
title={Incorporating toxin hypothesis into a mathematical model of persister formation and dynamics},
author={Cogan, NG},
journal={Journal of theoretical biology},
volume={248},
number={2},
pages={340--349},
year={2007},
publisher={Elsevier}
}
@article{cogan2008,
title={Two-fluid model of biofilm disinfection},
author={Cogan, NG},
journal={Bulletin of mathematical biology},
volume={70},
number={3},
pages={800--819},
year={2008},
publisher={Springer}
}
@article{Cogan2006,
author = {Cogan, N G},
doi = {10.1016/j.jtbi.2005.06.017},
issn = {0022-5193},
journal = {Journal of theoretical biology},
keywords = {Anti-Bacterial Agents,Anti-Bacterial Agents: pharmacology,Bacteria,Bacteria: cytology,Bacterial Infections,Bacterial Infections: transmission,Bacterial Physiological Phenomena,Biofilms,Dose-Response Relationship, Drug,Drug Resistance,Models, Biological},
month = feb,
number = {3},
pages = {694--703},
pmid = {16125727},
title = {{Effects of persister formation on bacterial response to dosing.}},
volume = {238},
year = {2006}
}
@article{Cogan2005,
author = {Cogan, N G and Cortez, Ricardo and Fauci, Lisa},
doi = {10.1016/j.bulm.2004.11.001},
issn = {0092-8240},
journal = {Bulletin of mathematical biology},
keywords = {Anti-Bacterial Agents,Anti-Bacterial Agents: pharmacology,Biofilms,Biofilms: growth \& development,Computer Simulation,Drug Resistance, Bacterial,Hypochlorous Acid,Hypochlorous Acid: pharmacology,Models, Biological,Pseudomonas aeruginosa,Pseudomonas aeruginosa: growth \& development,Rheology},
month = jul,
number = {4},
pages = {831--53},
pmid = {15893555},
title = {{Modeling physiological resistance in bacterial biofilms.}},
volume = {67},
year = {2005}
}
@article{Picioreanu1999,
author = {Picioreanu, Cristian and Loosdrecht, Van and {M Cheijnen}, J J},
doi = {10.1016/S0273-1223(99)00158-4},
issn = {02731223},
journal = {Water Science and Technology},
keywords = {biofilm,convection,diffusion,flow,multidimensional modelling,porosity,roughness,structure},
number = {7},
pages = {115--122},
publisher = {International Asssociation on Water Quality},
title = {{Discrete-differential modelling of biofilm structure}},
volume = {39},
year = {1999}
}
@article{murga1995,
title={Quantitative analysis of biofilm thickness variability},
author={Murga, Ricardo and Stewart, Philip S and Daly, Don},
journal={Biotechnology and bioengineering},
volume={45},
number={6},
pages={503--510},
year={1995},
publisher={Wiley Online Library}
}
@article{Chopp2007,
year={2007},
isbn={978-0-387-31201-9},
booktitle={Deformable Models},
series={Topics in Biomedical Engineering. International Book Series},
doi={10.1007/978-0-387-68413-0_1},
title={Simulating Bacterial Biofilms},
url={http://dx.doi.org/10.1007/978-0-387-68413-0_1},
publisher={Springer New York},
author={Chopp, DavidL.},
pages={1-31}
}
@article{Roberts2005,
author = {Roberts, Mark E and Stewart, Philip S},
doi = {10.1099/mic.0.27385-0},
issn = {1350-0872},
journal = {Microbiology (Reading, England)},
keywords = {Anti-Bacterial Agents,Anti-Bacterial Agents: pharmacology,Bacteria,Bacteria: cytology,Bacteria: drug effects,Bacteria: growth \& development,Bacterial,Biofilms,Biofilms: drug effects,Biofilms: growth \& development,Biological,Culture Media,Drug Resistance,Microbial Sensitivity Tests,Models,Plankton,Plankton: drug effects,Plankton: growth \& development},
month = jan,
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institution = {Vienna University of Technology},
mendeley-groups = {level set method},
pages = {90},
title = {{Extended finite element methods for interface problems}},
year = {2015}
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author = {{De Vuyst}, Florian},
file = {:Users/dinhanhthi/Dropbox/PhD/docs/freefem{\_}docs/numerical modeling transport problem with freefem - Florian De Vuyst.pdf:pdf},
institution = {ENS CACHAN},
pages = {162},
title = {{Numerical modeling of transport problems using freefem++ software -- with examples in biology, CFD, traffic flow and energy transfer}},
url = {http://cel.archives-ouvertes.fr/cel-00842234},
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