Accepted or published papers

  • Design of asymptotic preserving finite volume schemes for hyperbolic heat equation on unstructured meshes, C. Buet, B. Després, E. Franck, Numerische Mathematik, October 2012, Volume 122, Issue 2, pp 227-278. ( Published version ).
  • Asymptotic preserving schemes for Friedrichs systems with stiff relaxation on unstructured meshes: applications to the angular discretization models in linear transport, C. Buet, B. Després, E. Franck, Journal Scientific Computing, Volume 62 Issue 2, February 2015, Pages 371-398. ( Published version ).
  • Energy conservation and numerical stability for the reduced MHD models of the non-linear JOREK code, E. Franck, M. Hölzl, A. Lessig, E. Sonnendrücker. ( Preprint ), ( Published version ). ESAIM: M2AN Volume 49, Number 5, September-October 2015.
  • Proof of uniform convergence for a cell-centered AP discretization of the hyperbolic heat equation on general meshes, C. Buet, B. Després, E. Franck, T. Leroy. ( Preprint ), ( Published version ) Mathematics of computation, September 12, 2016.
  • Finite volume scheme with local high order discretization of hydrostatic equilibrium for Euler equations with external forces, E. Franck, L. Mendoza. ( Preprint ), ( Published version ) Journal of Scientific Computing, October 2016, Volume 69, Issue 1, pp 314-354
  • Stability of a Kirchhoff-Roe scheme for multi-dimensional linearized Euler systems, E. Franck, L. Gosse. ( Published version ), Annali Dell' Universita' Di Ferrara, December 2017.
  • An analysis of over-relaxation in kinetic approximation, F.Drui, E. Franck, P. Helluy, L. Navoret. ( Preprint ), ( Published version ). Accepted in "Comptes rendus Mécanique"
  • Accepted or published notes

  • An asymptotic preserving scheme with the maximum principle for the M1 model on distorted meshes, C. Buet, B. Després, E. Franck, Comptes Rendus Mathematique, Volume 350, Issues 11-12, June 2012, Pages 633-638. ( Published version ).
  • Accepted or published proceedings

  • An asymptotic preserving scheme for P1 model using classical diffusion schemes on unstructured polygonal meshes, E. Franck, P. Hoch, P. Navaro and G. Samba, ESAIM: PROCEEDINGS, October 2011, Vol. 32, p. 56-75. ( Published version ).
  • Asymptotic Preserving Finite Volumes Discretization For Non-Linear Moment Model On Unstructured Meshes, C. Buet, B. Després, E. Franck, Finite Volumes for Complex Applications VI Problems and Perspectives, Springer Proceedings in Mathematics Volume 4, 2011, pp 467-474. ( Published version ).
  • A priori analysis of asymptotic preserving schemes with the modified equation, B. Després (main author), C. Buet and E. Franck. Hyperbolic problems: theory, numerics and applications, AIMS on Applied Mathematics,vol 8, pp 501. ( First online version ).
  • Modified Finite Volume Nodal Scheme for Euler Equations with Gravity and Friction, E. Franck, Finite Volumes for Complex Applications VII-Methods and Theoretical Aspects Springer Proceedings in Mathematics & Statistics Volume 77, 2014, pp 285-292. ( Published version ).
  • Anisotropic diffusion in toroidal geometry , A. Ratnani, B. Nkonga, E. Franck, A. Eksaeva, M. Kazakova. ( Preprint ), ( Published version ) ESAIM Proc, Volume 53, March 2016, pp 77-98.
  • Study of physic-based preconditioning with high order Galerkin method discretization for hyperbolic wave problems, C. Courtes, E. Franck ,P. Helluy and H. Oberlin. ( Published version ). ESAIM: PROCEEDINGS AND SURVEYS, December 2016, Vol. 55, p. 61-82.
  • Palindromic discontinuous Galerkin method, D. Coulette, E. Franck, P. Helluy, M. Mehrenberger, L. Navoret. ( Published version ). FVCA 2017: Finite Volumes for Complex Applications VIII - Hyperbolic, Elliptic and Parabolic Problems, pp 171-178.
  • Task-based parallelization of an implicit kinetic scheme, J. Badwaik, M. Boileau, D. Coulette, E. Franck, P. Helluy, L. Mendoza, H. Oberlin. ( Preprint ), ( Published version ).
  • Preprint or submitted papers and proceedings

  • High-order implicit palindromic discontinuous Galerkin method for kinetic-relaxation approximation, D. Coulette, E. Franck, P. Helluy, M. Mehrenberger, L. Navoret. ( Preprint ). Submit in in "Computer and fluids".
  • Implicit time schemes for compressible fluid models based on relaxation methods, D. Coulette, E. Franck, P. Helluy, A. Ratnani, E. Sonnendruecker. ( Preprint ), Submit in "Computer and fluids".
  • Vectorial kinetic relaxation model with central velocity. Application to implicit relaxations schemes , D. Coulette, C. Courtès, E. Franck, L. Navoret. ( Preprint ), Submit in "Communications in computational physics".
  • Linear stability of a vectorial kinetic relaxation scheme with a central velocity , C. Courtès, E. Franck. ( Preprint ), Submit in "HYP2018 proceedings".
  • Papers in preparation

  • Implicit splitted Compatible finite element scheme for MHD, E. Franck, M. Gaja, A. Ratnani, E. Sonnendruecker. In redaction.
  • Diffusion terms in vectorial Lattice Boltzmann scheme C. Klingenberg, E. Franck, P. Helluy, L. Thanhäuser. In redaction.
  • Vectorial Lattice Boltzmann scheme for MHD C. Klingenberg, F.Drui, E. Franck, P. Helluy. In redaction.
  • Semit implicit relaxation scheme for low mach Euler equations, F. Bouchut, E. Franck, L. Navoret. In redaction.
  • Participation in physical papers

  • Mechanism of Edge Localized Mode mitigation by Resonant Magnetic Perturbations, M. Bécoulet, F. Orain, X. Garbet, G. T. A Huijsmans, S. Pamela, P. Cahyna, M. Hölzl, E. Franck, E. Sonnendrücker, G. Dif-Pradalier, C. Passeron, G. Latu, J. Morales, E. Nardon, A. Fil, B. Nkonga, A. Ratnani, Phys. Rev. Lett. 113, 155001, september 2014. ( Published version ).
  • Other

  • Participation to Oberwolfach workshop report: Time implicit schemes for the JOREK MHD code: Newton procedure, continuation and preconditioning, E. Franck, E. Sonnendrücker, M. Hölzl.