Publications

2009

• Numerical resolution of the wave equation on a network of slots
  
  • Semin Adrien
  , 2009, pp.35. In this technical report, we present a theoretical and numerical model to simulate wave propagation in finite networks of rods with both classical Kirchhoff conditions and Improved Kirchhoff conditions at the nodes of the networks. One starts with the continuous framework, then we discretize the problem using finite elements with the mass lumping technic introduced by G.~Cohen and P.~Joly. Finally, we show an implementation of the obtained numeric scheme in a homemade code written in C++ in collaboration with K.~Boxberger, some results and some error estimates.
• Space-time mesh refinement for discontunuous Galerkin methods for symmetric hyperbolic systems
  
  • Ezziani Abdelaâziz
  • Joly Patrick
  Journal of Computational and Applied Mathematics, Elsevier, 2009, 234 (6), pp.1886-1895. We present a new non-conforming space-time mesh refinement method for the symmetric first order hyperbolic system. This method is based on the one hand on the use of a conservative higher order discontinuous Galerkin approximation for space discretization and a finite difference scheme in time, on the other hand on appropriate discrete transmission conditions between the grids. We use a discrete energy technique to drive the construction of the matching procedure between the grids and guarantee the stability of the method. (10.1016/j.cam.2009.08.094)
  DOI : 10.1016/j.cam.2009.08.094