ERROR ESTIMATES FOR A NONLINEAR LOCAL PROJECTION STABILIZATION OF TRANSIENT CONVECTION-DIFFUSION-REACTION EQUATIONS

作者：Knobloch Peter^*

来源：Discrete and Continuous Dynamical Systems - Series S, 2015, 8(5): 901-911.

DOI：10.3934/dcdss.2015.8.901

• Finite element method
• local projection stabilization
• crosswind diffusion
• transient convection-diffusion-reaction equation
• well posedness
• error estimates

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.

• 出版日期2015-10