Publications

2008

• A characterization of singular electromagnetic fields by an inductive approach
  
  • Assous F.
  • Ciarlet Patrick
  • Garcia E.
  International Journal of Numerical Analysis and Modeling, Institute for Scientific Computing and Information, 2008, 5 (3), pp.491-515. In this article, we are interested in the mathematical modeling of singular electromagnetic fields, in a non-convex polyhedral domain. We first describe the local trace (i. e. defined on a face) of the normal derivative of an L2 function, with L2 Laplacian. Among other things, this allows us to describe dual singularities of the Laplace problem with homogeneous Neumann boundary condition. We then provide generalized integration by parts formulae for the Laplace, divergence and curl operators. With the help of these results, one can split electromagnetic fields into regular and singular parts, which are then characterized. We also study the particular case of divergence-free and curl-free fields, and provide non-orthogonal decompositions that are numerically computable. © 2008 Institute for Scientific Computing and Information.
• A monotonic evaluation of lower bounds for inf-sup stability constants in the frame of reduced basis approximations
  
  • Chen Yanlai
  • Hesthaven Jan S.
  • Maday Yvon
  • Rodríguez Jerónimo
  Comptes Rendus. Mathématique, Académie des sciences (Paris), 2008, 346 (23-24), pp.1295-1300. For accurate a posteriori error analysis of the reduced basis method for coercive and non-coercive problems, a critical ingredient lies in the evaluation of a lower bound for the coercivity or inf-sup constant. In this short Note, we generalize and improve the successive constraint method first presented by Huynh (2007) by providing a monotonic version of this algorithm that leads to both more stable evaluations and fewer offline computations. © 2008 Académie des sciences. (10.1016/j.crma.2008.10.012)
  DOI : 10.1016/j.crma.2008.10.012