List of Publications

Alexandre Ern

• 2010
  • A. Bourlioux, AE and P. Turbis, A posteriori error estimation for subgrid flamelet models, Multiscale Model. Simul., 8(2), 481--497 (2010).
  • D. A. Di Pietro and AE, Discrete functional analysis tools for Discontinuous Galerkin methods with application to the incompressible Navier--Stokes equations, Math. Comp., to appear (2010).
  • D. Doyen, AE and S. Piperno, A three-field augmented Lagrangian formulation of unilateral contact problems with cohesive forces, ESAIM Math. Mod. Numer. Anal., to appear (2010).
  • AE, I. Mozolevski and L. Schuh, Discontinuous Galerkin approximation of two-phase flows in heterogeneous porous media with discontinuous capillary pressures, Comp. Meth. Appl. Mech. Eng., to appear (2010).
  • AE, A. F. Stephansen and M. Vohralík, Guaranteed and robust discontinuous Galerkin a posteriori error estimates for convection--diffusion--reaction problems, J. Comput. Appl. Math., 234, 114--130 (2010).
  • AE and M. Vohralík, A posteriori error estimation based on potential and flux reconstruction for the heat equation, SIAM J. Numer. Anal., to appear (2010).
  • S. Perotto, AE and A. Veneziani, Hierarchical local model reduction for elliptic problems: A domain decomposition approach, Multiscale Model. Simul., to appear (2010).
• 2009
  • B. Achchab, M. El Fatini, AE and A. Souissi, A posteriori error estimates for subgrid viscosity stabilized approximations of convection-diffusion equations, Appl. Math. Letters, 22, 1418--1424 (2009).
  • F. Chazel, M. Benoit, AE and S. Piperno, A double-layer Boussinesq-type model for highly nonlinear and dispersive waves, Proc. R. Soc. A, 465, 2319--2346 (2009).
  • D. Doyen and AE, Convergence of a space semi-discrete modified mass method for the dynamic Signorini problem, Comm. Math. Sciences, 7(4), 1063--1074 (2009).
  • AE and S. Meunier, A posteriori error analysis of Euler--Galerkin approximations to coupled elliptic--parabolic problems, ESAIM Math. Mod. Numer. Anal., 43, 353--375 (2009).
  • AE, I. Mozolevski and L. Schuh, Accurate velocity reconstruction for Discontinuous Galerkin approximations of two-phase porous media flows, C. R. Acad. Sci. Paris, Ser. I, 347, 551--554 (2009).
  • AE, A. F. Stephansen and P. Zunino, A Discontinuous Galerkin method with weighted averages for advection--diffusion equations with locally small and anisotropic diffusivity, IMA J. Numer. Anal., 29(2), 235--256 (2009).
  • AE and M. Vohralík, Flux reconstruction and a posteriori error estimation for discontinuous Galerkin methods on general nonmatching grids, C. R. Acad. Sci. Paris, Ser. I, 347, 441--444 (2009).
  • P. Sochala, AE and S. Piperno, Mass conservative BDF-discontinuous Galerkin/explicit finite volume schemes for coupling subsurface and overland flows, Comp. Meth. Appl. Mech. Eng., 198, 2122--2136 (2009).
• 2008
  • B. Achchab, M. El Fatini, AE and A. Souissi, Adaptive mesh for algebraic orthogonal subscale stabilization of convective dispersive transport, C. R. Acad. Sci. Paris, Ser. I, 346, 1187--1190 (2008).
  • E. Burman and AE, Discontinuous Galerkin approximation with discrete variational principle for the nonlinear Laplacian, C. R. Acad. Sci. Paris, Ser. I, 346(17/18), 1013--1016 (2008).
  • D. Di Pietro, AE and J.-L. Guermond, Discontinuous Galerkin methods for anisotropic semi-definite diffusion with advection, SIAM J. Numer. Anal., 46(2), 805--831 (2008).
  • AE and J.-L. Guermond, Discontinuous Galerkin methods for Friedrichs' systems. III. Multi-field theories with partial coercivity, SIAM J. Numer. Anal., 46(2), 776--804 (2008).
  • A. Ern, S. Piperno and K. Djadel, A well-balanced Runge--Kutta Discontinuous Galerkin method for the Shallow-Water Equations with flooding and drying, Int. J. Numer. Meth. Fluids, 58(1), 1--25 (2008).
  • AE and A. F. Stephansen, A posteriori energy-norm error estimates for advection-diffusion equations approximated by weighted interior penalty methods, J. Comp. Math., 26(4), 488--510 (2008).

• 2007
  • E. Burman and AE, Continuous interior penalty $hp$-finite element methods for advection and advection--diffusion equations, Math. Comp., 76(259), 1119--1140 (2007).
  • E. Burman and AE, A continuous finite element method with face penalty to approximate Friedrichs' systems, ESAIM Math. Mod. Numer. Anal., 41(1), 55--76 (2007).
  • E. Burman, AE, I. Mozolevski and B. Stamm, The symmetric discontinuous Galerkin method does not need stabilization in 1D for polynomial orders p >= 2, C. R. Acad. Sci. Paris, Ser. I, 345, 599--602 (2007).
  • L. El Alaoui, AE and E. Burman, A priori and a posteriori analysis of nonconforming finite elements with face penalty for advection--diffusion equations, IMA J. Numer. Anal., 27(1), 151--171 (2007).
  • AE, J.-L. Guermond and G. Caplain, An intrinsic criterion for the bijectivity of Hilbert operators related to Friedrichs' systems, Comm. Partial Differ. Equations, 32, 317--341 (2007).
  • AE and T. Lelièvre, Adaptive models for polymeric fluid flow simulation, C. R. Acad. Sci. Paris, Ser. I, 344(7), 473--476 (2007).
  • AE, S. Nicaise and M. Vohralík, An accurate H(\rm div) flux reconstruction for discontinuous Galerkin approximations of elliptic problems, C. R. Acad. Sci. Paris, Ser. I, 345, 709--712 (2007).
  • P. Tardif d'Hamonville, AE and L. Dormieux, Finite element evaluation of diffusion and dispersion tensors in periodic porous media with advection, Comput. Geosci., 11, 43--58 (2007).

• 2006
  • H. Beaugendre, AE, Th. Esclaffer, E. Gaume, I. Ginzburg and C. Kao, A seepage face model for the interaction of shallow water tables with ground surface: Application of the obstacle-type method, J. Hydrology, 329(1/2), 258--273 (2006).
  • L. Debiane, B. Ivorra, B. Mohammadi, F. Nicoud, T. Poinsot, AE and H. Pitsch, A low-complexity global optimization algorithm for temperature and pollution control in flames with complex chemistry, Int. J. Comput. Fluid Dynamics, 20(2), 93--98 (2006).
  • L. El Alaoui and AE, Nonconforming finite element methods with subgrid viscosity applied to advection--diffusion--reaction equations, Num. Methods Partial Differential Equations, 22(5), 1106--1126 (2006).
  • AE and J.-L. Guermond, Discontinuous Galerkin methods for Friedrichs' systems. I. General theory, SIAM J. Numer. Anal., 44(2), 753--778 (2006).
  • AE and J.-L. Guermond, Discontinuous Galerkin methods for Friedrichs' systems. II. Second-order elliptic PDE's, SIAM J. Numer. Anal., 44(6), 2363--2388 (2006).
  • AE and J.-L. Guermond, Evaluation of the condition number in linear systems arising in finite element approximations, ESAIM Math. Mod. Numer. Anal., 40(1), 29--48 (2006).
  • AE and J. Proft, Multi-algorithmic methods for coupled hyperbolic-parabolic problems, Int. J. Numer. Anal. Model., 3(1), 94--114 (2006).

• 2005
  • E. Burman and AE, Stabilized Galerkin approximation of convection-diffusion-reaction equations: discrete maximum principle and convergence, Math. Comp., 74(252), 1637--1652 (2005).
  • J.-P. Croisille, AE, T. Lelièvre and J. Proft, Analysis and simulation of a coupled hyperbolic/parabolic model problem, J. Numer. Math., 13(2), 81--103 (2005).
  • A.S. Dickinson, AE and V. Vesovic, Transport properties of H--N$_2$ mixtures, Mol. Phys., 103(14), 1895--1904 (2005).
  • AE, A.S. Dickinson and V. Vesovic, A compact formulation for multi-component transport coefficients in gas mixtures, Chem. Phys., 310, 311--319 (2005).
  • AE and J. Proft, A posteriori discontinuous Galerkin error estimates for transient convection-diffusion equations, Appl. Math. Letters, 18, 833--841 (2005).

• 2000-2004
  • E. Bongiovanni, AE and N. Glinsky-Olivier, Evaluation of an energy relaxation method for the simulation of unsteady, viscous, real gas flows, Int J. Num. Meth. Fluids, 45, 1025--1046 (2004).
  • M. Braack and AE, Coupling multimodeling with local mesh refinement for the numerical computation of laminar flames, Combust. Theory Model., 8(4), 771--788 (2004).
  • E. Burman and AE, Discrete maximum principle for Galerkin approximations of the Laplace operator on arbitrary meshes, C. R. Acad. Sci. Paris, Sér. I, 338, 641--646 (2004).
  • E. Burman, AE and V. Giovangigli, Bunsen flame simulation by finite elements on adaptively refined, unstructured triangulations, Combust. Theory Model., 8(1), 65--84 (2004).
  • L. El Alaoui and AE, Residual and hierarchical a posteriori error estimates for nonconforming mixed finite element methods, ESAIM Math. Mod. Numer. Anal., 38(6), 903--929 (2004).
  • AE, A.S. Dickinson and V. Vesovic, On the behavior of the volume viscosity of atom-molecule mixtures, J. Chem. Phys., 121(17), 8658--8660 (2004).
  • AE and J.-L. Guermond, Accurate numerical simulation of radiative heat transfer with application to crystal growth, Int. J. Num. Meth. Eng., 61, 559--583 (2004).
  • AE, S. Villeneuve and A. Zanette, Adaptive finite element methods for local volatility European option pricing, Int. J. Theor. Appl. Finance, 7(6), 659--684 (2004).
  • E. Bongiovanni, AE and N. Glinsky-Olivier, Une nouvelle méthode de relaxation pour les équations de Navier-Stokes compressibles, C. R. Acad. Sci. Paris, Sér. I, 336, 283--288 (2003).
  • E. Bongiovanni, AE and N. Glinsky-Olivier, A new relaxation method for the compressible Navier-Stokes equations, Math. Meth. Models Appl. Sci., 13(10), 1379--1396 (2003).
  • M. Braack and AE, A posteriori control of modeling errors and discretization errors, Multiscale Model. Simul., 1(2), 221--238 (2003).
  • E. Burman, AE and V. Giovangigli, An adaptive finite element method with crosswind diffusion for low Mach, steady, laminar combustion, J. Comput. Phys., 188(2), 472--492 (2003).
  • AE and V. Giovangigli, Kinetic theory of reactive gas mixtures with application to combustion, Transp. Theory Stat. Phys., 32(5-7), 657--677 (2003).
  • E. Burman and AE, Nonlinear diffusion and discrete maximum principle for stabilized Galerkin approximations of the convection-diffusion-reaction equation, Comp. Meth. Appl. Mech. Eng., 191, 3833--3855 (2002).
  • J. de Charentenay and AE, Multicomponent transport impact on turbulent premixed H$_2$/O$_2$ flames, Combust. Theory Model., 6, 439--462 (2002).
  • AE and V. Giovangigli, Comment on ''Different levels of modeling for diffusion phenomena in neutral and ionized gas mixtures'', J. Thermophysics Heat Transfer, AIAA, 14(1), 119--120, (2000).

• 1993-2000
  • AE and V. Giovangigli, Impact of detailed multicomponent transport on planar and counterflow hydrogen/air and methane/air flames, Combust. Sci. and Tech., 149, 157--181 (1999).
  • AE, J.-L. Guermond, and L. Quartapelle, Vorticity-velocity formulations of the Stokes problem in 3D, Math. Meth. Appl. Sci., 22, 531--546 (1999).
  • AE, Vorticity-velocity formulation of the Stokes problem with variable density and viscosity, Math. Meth. Models Appl. Sci., 8, 203--218 (1998).
  • AE and V. Giovangigli, The kinetic chemical equilibrium regime, Physica A, 260, 49--72 (1998).
  • AE and V. Giovangigli, Thermal diffusion effects in hydrogen/air and methane/air flames, Combust. Theory Model., 2, 349--372 (1998).
  • C.C. Douglas, AE, and M.D. Smooke, Numerical solution of flame sheet problems on serial and parallel computers, Parallel Alg. Appl., 10, 225--236 (1997).
  • AE, Detailed modeling and sensitivity analysis of a rotating disk MOCVD reactor, J. Chem. Vapor Depos., 5, 237--266 (1997).
  • AE and V. Giovangigli, Projected iterative algorithms with application to multicomponent transport, Linear Algebra Appl., 250, 289--315 (1997).
  • AE, V. Giovangigli, and M.D. Smooke, Detailed modeling of three-dimensional chemical vapor deposition, J. Crystal Growth, 180, 670--679 (1997).
  • AE, Vorticity-velocity formulation of the Stokes problem with variable density and viscosity, C. R. Acad. Sci. Paris, Sér. I, 323, 1159--1164 (1996).
  • AE, Sur la formulation tourbillon-vitesse des équations de Navier-Stokes avec densité et viscosité variables, C. R. Acad. Sci. Paris, Sér. IIb, 323, 813--818 (1996).
  • AE and V. Giovangigli, The structure of transport linear systems in dilute isotropic gas mixtures, Phys. Rev. E, 53, 485--492 (1996).
  • AE and V. Giovangigli, Kinetic theory of dilute gas mixtures with independent internal energy modes near equilibrium, Physica A, 224, 613--625 (1996).
  • AE and V. Giovangigli, Optimized transport algorithms for flame codes, Combust. Sci. and Tech., 118, 387--395 (1996).
  • AE, V. Giovangigli, and M.D. Smooke, Numerical study of a three-dimensional chemical vapor deposition reactor with detailed chemistry, J. Comput. Phys., 126, 21--39 (1996).
  • AE, C.C. Douglas, and M.D. Smooke, Detailed chemistry modeling of laminar diffusion flames on parallel computers, Int. J. Supercomput. Appl., 9, 167--186 (1995).
  • AE and V. Giovangigli, Thermal conduction and thermal diffusion in dilute polyatomic gas mixtures, Physica A, 214, 526--546 (1995).
  • AE and V. Giovangigli, Fast and accurate multicomponent transport property evaluation, J. Comput. Phys., 120, 105--116 (1995).
  • AE and V. Giovangigli, Volume viscosity of dilute polyatomic gas mixtures, European J. Mech., B/Fluids, 14, 653--669 (1995).
  • AE and V. Giovangigli, On the evaluation of thermal diffusion coefficients in chemical vapor deposition processes, J. Chem. Vapor Depos., 3, 3--31 (1995).
  • C.C. Douglas, AE, and M.D. Smooke, Parallelizing the numerical solution of laminar diffusion flames, SIAM Newsjournal, 27 (1994).
  • AE, V. Giovangigli, D.E. Keyes, and M.D. Smooke, Towards polyalgorithmic linear system solvers for nonlinear elliptic systems, SIAM J. Sci. Comput., 15, 681--703 (1994).
  • AE and M.D. Smooke, Vorticity-velocity formulation for three-dimensional steady compressible flows, J. Comput. Phys., 105, 58--71 (1993).