Local projection stabilization virtual element method for the convection-diffusion equation with nonlinear reaction term

Abstract

We present an efficient local projection-based stabilized virtual element method for the convection-diffusion equation with a nonlinear reaction term. The proposed discrete scheme contains a local projection stabilization term with a suitable virtual element stabilizer. We prove the existence and stability of the discrete solution and then the convergence estimates in the energy and L2 norms. Numerical experiments are conducted for the problems having interior and boundary layers. We validate the theoretical convergence rates and show the efficiency of the proposed method by comparing the obtained results with the residual-based stabilization methods.