Virtual element method for nonlinear convection–diffusion–reaction equation on polygonal meshes

ABSTRACT

In this paper, we discuss the virtual element formulation for the nonlinear convection–diffusion–reaction equation. We consider the Streamline upwind Petrov–Galerkin stabilization to reduce the non-physical oscillations presented in the solution. The nonlinear term is evaluated after a suitable modification with the help of a polynomial projection operator. We perform the error analysis by showing the existence of the solution and derive the convergence estimates in the energy norm. Numerical experiments are conducted in order to validate the theoretical results.

Keywords:

• Virtual element
• nonlinear convection–diffusion–reaction equation
• SUPG stabilization
• error estimates
• polygonal meshes

2010 AMS Subject Classifications:

• 65N12
• 65N30

Disclosure statement

No potential conflict of interest was reported by the author(s).