Error estimates for a nonlinear local projection stabilization of transient convection-diffusion-reaction equations
2015
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.