Department of Numerical Mathematics Faculty of Mathematics and Physics Charles University

Error estimates for a nonlinear local projection stabilization of transient convection-diffusion-reaction equations

  • ID: 2714, RIV: 10318482
  • ISSN: 1937-1632, ISBN: not specified
  • source: Discrete and Continuous Dynamical Systems - Series S
  • keywords: Finite element method; local projection stabilization; crosswind diffusion; transient convection-diffusion-reaction equation; well posedness; error estimates
  • authors: Petr Knobloch
  • authors from KNM: Knobloch Petr


A recently proposed local projection stabilization (LPS) finite element method containing a nonlinear crosswind diffusion term is analyzed for a transient convection-diffusion-reaction equation using a one-step theta-scheme as temporal discretization. Both the fully nonlinear method and its semi-implicit variant are considered. Solvability of the discrete problem is established and a priori error estimates in the LPS norm are proved. Uniqueness of the discrete solution is proved for the semi-implicit approach or for sufficiently small time steps.