### PhD: Bibliography

Posted on 07/06/2017, in PhD.

Chú ý rằng những id trong đây cũng là những id được dùng trong các file tex.

• Carraro2016 On the implementation of the eXtended Finite Element Method ( XFEM ) for interface problems
• Capatina2017 Extension of NXFEM to nonconforming finite elements
• Areias2006 A comment on the article “A finite element method for simulation of strong and weak discontinuities in solid mechanics” by A. Hansbo and P. Hansbo [Comput. Methods Appl. Mech. Engrg. 193 (2004) 3523-3540]
• Capatina2015 Nonconforming ﬁnite element approximation of an elliptic interface problem with NXFEM
• Burman2014 CutFEM: Discretizing geometry and partial differential equations
• Burman2009 Fictitious domain ﬁnite element methods using cut elements: II. A stabilized Nitsche method
• Eymard2010 Discretization of heterogeneous and anisotropic diffusion problems on general nonconforming meshes
• DiPietro2010 Discrete functional analysis tools for Discontinuous Galerkin methods with application to the incompressible Navier–Stokes equations
• Ainsworth1997 A posteriori error estimation in finite element analysis
• Debnath2005 Hilbert spaces with applications
• Leoni2009 A first course in Sobolev spaces
• Baratchart2016 Uniqueness results for inverse Robin problems with bounded coefficient
• Duddu2006 A combined extended finite element and level set method for biofilm growth
• El-Otmany2015 : [thesis] Approximation by NXFEM method of interphase and interface problems in fluid mechanics
• Duddu2008 A two-dimensional continuum model of biofilm growth incorporating fluid flow and shear stress based detachment
• Mah2001 Mechanisms of biofilm resistance to antimicrobial agents
• Chopp2002 A mathematical model of quorum sensing in a growing bacterial biofilm
• Thomee2006 Galerkin Finite Element Methods for Parabolic Problems
• Knabner2002 Numerical Methods for Elliptic and Parabolic Partial Differential Equations
• Hysing2007 : THESIS Numerical Simulation of Immiscible Fluids with FEM Level Set Techniques
• Picioreanu2000 Effect of diffusive and convective substrate transport on biofilm structure formation: a two-dimensional modeling study
• Rittma1982 The Effect of Shear Stress on Bioflm Loss Rate
• Cogan2006 Effects of persister formation on bacterial response to dosing
• Cogan2005 Modeling physiological resistance in bacterial biofilms
• Picioreanu1999 Discrete-differential modelling of biofilm structure
• Chopp2007 Simulating Bacterial Biofilms
• Roberts2005 Modelling protection from antimicrobial agents in biofilms through the formation of persister cells
• Davies2003 Understanding biofilm resistance to antibacterial agents
• Chen1998 Finite element methods and their convergence for elliptic and parabolic interface problems
• Bramble1996 A finite element method for interface problems in domains with smooth boundaries and interfaces
• Babuska1970 The finite element method for elliptic equations with discontinuous coefficients
• Ladyzhenskaya1966 The solvability of diffraction problems
• Li2003 New Cartesian grid methods for interface problems using the finite element formulation
• Sinha An unfitted finite-element method for elliptic and parabolic interface problems
• Wu An unfitted hp -interface penalty finite element method for elliptic interface problems
• Hansbo2002 An unfitted finite element method, based on Nitsche’s method, for elliptic interface problems
• Barrau2012 A robust variant of NXFEM for the interface problem
• Wang2014 An Unfitted Discontinuous Galerkin Method for Elliptic Interface Problems
• Smith2007 The extended finite element method for boundary layer problems in biofilm grown
• Engwer2009 An Unfitted Discontinuous Galerkin Scheme for Micro-scale Simulations and Numerical Upscaling
• nitscheIdea What is the general idea of Nitsche’s method in numerical analysis
• Barrau2013 [Thesis] Généralisation de la méthode Nitsche XFEM pour la discétisation de problèmes d’interface elliptiques
• LeDret2013 Équations Aux Dé}rivées Partielles Elliptiques Non Liné}aires
• Ishihara1982 Finite Element Approximations Applied to the Nonlinear Boundary Value Problem $\Delta u=bu^2$
• Ern2004 Theory and Practice of Finite Elements
• Rudin Real and complex analysis
• Vasile2007 Iterative Approximation of Fixed Points, Lecture Notes in Mathematics
• Bui2011 A coupling strategy based on anisotropic mesh adaptation for solving two-fluid flows
• Bui2009 Simulation des écoulements bifluides, une stratégie de couplage basée sur l’adaptation de maillage anisotrope
• Hesthaven2008 Nodal Discontinuous Galerkin Methods
• ArnoldBook Numerical methods for two-phase incompressible flows
• Li2003 An overview of the immersed interface method and its applications
• Osher1988 Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations
• Tornberg2000 A finite element based level-set method for multiphase flow applications
• Sussman1994 A Level Set Approach for Computing Solutions to Incompressible Two-Phase Flow
• Lehrenfeld2015 Extended finite element methods for interface problems
• Lehrenfeld2012 Nitsche-XFEM with Streamline Diffusion Stabilization for a Two-Phase Mass Transport Problem
• Arnold2008 Analysis of an extended pressure finite element space for two-phase incompressible flows
• Lehrenfeld2014 Optimal preconditioners for Nitsche-XFEM discretizations of interface problems
• DeVuyst2013 Numerical modeling of transport problems using freefem++ software – with examples in biology, CFD, traffic flow and energy transfer
• Loch2013 The level set method for capturing interfaces with applications in two-phase flow problems
• Hieu2009 Nitsche’s method for a transport problem in two phase incompressible flow
• Lehrenfeld2011 Nitsche-XFEM for a transport problem in two-phase incompressible flows
• HieuThesis Numerical methods for mass transport equations in two-phase incompressible flows
• Burman2010 Ghost penalty
• Sethian1999 The Fast Construction of Extension Velocities in Level Set Methods
• Sethian2003 Level set methods for fluid interface
• Hou1996 Eulerian Capturing Methods Based on a Level Set Formulation for Incompressible Fluid Interfaces
• Dolejsi2015 Discontinuous Galerkin Method
• Arnold2001 Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems
• Chopp2003 The dependence of quorum sensing on the depth of a growing biofilm
• Brezzi2004 Discontinuous Galerkin Methods for First-Order Hyperbolic Problems
• ErnDiscont Mathematical Aspects of Discontinuous Galerkin methods
• Nitsche1971 Uber ein Variationsprinzip zur Losung von Dirichlet-Problemen bei Verwendung von Teilraumen, die keinen Randbedingungen unterworfen sind
• Kubinska2005 Approximation of Carathéodory functions and multifunctions
• LongChen : Programming of finite element methods in Matlab (link).
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