Osher S., Sethian J.A. Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations. J Comput Phys 1988, 79(1):12-49.
Thömmes G., Becker J., Junk M., Vaikuntam A.K., Kerhwald D., Klar A., et al. A lattice Boltzmann method for immiscible multiphase flow simulations using the level set method. J Comput Phys 2009, 228:1139-1156.
Kim H., Liou M.-S. Accurate adaptive level set method and sharpening technique for three-dimensional deforming interfaces. Comput Fluids 2011, 44:111-129.
Olsson E., Kreiss G. A conservative level set method for two-phase flow. J Comput Phys 2008, 210:225-246.
Sussman M., Smith K.M., Hussaini M.Y., Ohta M., Zhi-Wei R. A sharp interface method for incompressible two-phase flows. J Comput Phys 2007, 221(2):469-505.
Marchandise E., Remacle J.-F. A stabilized finite element method using a discontinuous level set approach for solving two phase incompressible flows. J Comput Phys 2006, 219:780-800.
Ville L., Silva L., Coupez T. Convected level set method for the numerical simulation of fluid buckling. Int J Numer Methods Fluids 2010, 1-6.
Bolotnov I.A., Jansen K.E., Drew D.A., Oberai A.A., Lahey R.T., Podowski M.Z. Detached direct numerical simulations of turbulent two-phase bubbly channel flow. Int J Multiphase Flow 2011, 37(6):647-659.
Marchandise E., Remacle J.-F., Cheveaugeon N. A quadrature-free discontinuous Galerkin method for the level set equation. J Comput Phys 2006, 212:338-357.
Marchandise E., Chevaugeon N., Remacle J.-F. Spatial and spectral superconvergence of discontinuous Galerkin method for hyperbolic problems. J Comput Appl Math 2008, 215(2):484-494.
Van Der Pijl S.P., Segal A., Vuik C., Wesseling P. A mass-conserving level set method for modeling of multi-phase flows. Int J Numer Methods Fluids 2005, 47(4):339-361.
Walker C, Müller B. A conservative level set method for sharp interface multiphase flow simulation. In: ECCOMAS CFD 2010 - 5th European conference on computational fluid dynamics; June 2010.
Grooss J., Hesthaven J.S. A level set discontinuous Galerkin method for free surface flows. Comput Methods Appl Mech Eng 2006, 195:3406-3429.
Sauerland H., Fries T.-P. The extended finite element method for two-phase and free-surface flows: a systematic study. J Comput Phys 2011, 230(9):3369-3390.
Sussman M., Smereka P., Osher S. A level set approach for computing solutions to incompressible two-phase flow. J Comput Phys 1994, 114:146-159.
Rouy E., Tourin A. A viscosity solutions approach to shape-from-shading. SIAM J Numer Anal 1992, 29(3):867-884.
Cockburn B., Gopalakrishnan J., Lazarov R. Unified hybridization of discontinuous Galerkin, mixed and continuous Galerkin methods for second order elliptic problems. SIAM J Numer Anal 2009, 47:1319-1365.
Peraire J, Nguyen NC, Cockburn B. A hybridizable discontinuous Galerkin method for the compressible Euler and Navier-Stokes equations (AIAA Paper 2010-363). In: Proceedings of the 48th AIAA aerospace sciences meeting and exhibit, Orlando, Florida; 2010.
Nguyen N.C., Peraire J., Cockburn B. An implicit high-order hybridizable discontinuous Galerkin method for the incompressible Navier-Stokes equations. J Comput Phys 2011, 230(4):1147-1170.
Cockburn B., Kanschat G., Schötzau D. A locally conservative LDG method for the incompressible Navier-Stokes equations. Math Comput 2005, 74(251):1067-1096.
Cockburn B., Shu C.-W. The local discontinuous Galerkin method for time-dependent convection-diffusion systems. SIAM J Numer Anal 1998, 35:2440-2463.
Cockburn B., Kanschat G., Schötzau D. Local discontinuous Galerkin methods for the Oseen equations. Math Comput 2003, 73(246):569-593.
Chorin A.J. A numerical method for solving incompressible viscous flow problems. J Comput Phys 1967, 2(1):12-26.
Bassi F., Crivellini A., Di Pietro D.A., Rebay S. An artificial compressibility flux for the discontinuous Galerkin solution of the incompressible Navier-Stokes equation. J Comput Phys 2006, 218(2):794-815.
Montlaur A., Fernandez-Mendez S., Peraire J., Huerta A. Discontinuous Galerkin methods for the Navier-Stokes equations using solenoidal approximations. Int J Numer Methods Fluids 2010, 64(5):549-564.
Rivière B. Discontinuous Galerkin methods for solving elliptic and parabolic equations: theory and implementation. Front Appl Math 2008, vol. 35:131-143. SIAM, [chapter 7].
Warburton T., Hesthaven J.S. On the constants in hp-finite element trace inverse inequalities. Comput Methods Appl Mech Eng 2003, 192:2765-2773.
Shahbazi K. An explicit expression for the penalty parameter of the interior penalty method (short note). J Comput Phys 2005, 205:401-407.
Hillewaert K, Remacle J-F, Drosson M. Sharp constants in the hp-finite element trace inverse inequality for standard functional spaces on all element types in hybrid meshes. SIAM J Numer Anal; submitted for publication.
Lax P.D. Weak solutions of nonlinear hyperbolic equations and their numerical computation. Commun Pure Appl Math VII 1954, 159-193.
Remacle J-F., Chevaugeon N., Marchandise E., Geuzaine C. Efficient visualization of high order finite elements. Int J Numer Methods Eng 2005.
ANN library; 2012. <. http://www.cs.umd.edu/mount/ANN/.
Cockburn B. High-order methods for computational physics. Lecture notes in computational science and engineering, chapter discontinuous Galerkin methods for convection-dominated problems 1999, vol. 9:69-224. Springer.
Jaffre J., Johnson C., Szepessy A. Convergence of the discontinuous Galerkin finite element method for hyperbolic conservation laws. Math Models Methods Appl Sci 1995, 5(3):367-386.
Bassi F., Cecchi F., Franchina N., Rebay S., Savini M. High-order discontinuous Galerkin computation of axisymmetric transonic flows in safety relief valves. Comput Fluids 2011, 49(1):203-213.
Cockburn B., Lin S.-Y., Shu C.-W. TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws III: One-dimensional systems. J Comput Phys 1989, 84(1):90-113.
Chandrasekhar S. Hydrodynamic and hydromagnetic stability 1961, Clarendon Press, Oxford.
Popinet S., Zaleski S. A front-tracking algorithm for accurate representation of surface tension. Int J Numer Methods Fluids 1999, 30:775-793.
Puckett G., Almgren A.S., Bell J.B., Marcus D.L., Rider W.J. A high-order projection method for tracking fluid interfaces in variable density incompressible flows. J Comput Phys 1997, 130:269-282.
He X., Chen S., Zhang R. A lattice Boltzmann scheme for incompressible multiphase flow and its application in simulation of Rayleigh Taylor instability. J Comput Phys 1999, 152:642-663.
Zhang Y.T., Shi J., Shu C.W., Zhou Y. Numerical viscosity and resolution of high-order weighted essentially nonoscillatory schemes for compressible flows with high reynolds numbers. Phys Rev E 2003, 68(4):046709.
ElmerFEM (CSC IT for science); 2011. <. http://www.csc.fi/english/pages/elmer.
Buresti G. Notes on the role of viscosity, vorticity and dissipation in incompressible flows. Meccanica 2009, 44(4):469-487.