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

Abstract

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.