Abstract
In this paper, the streamline upwind/Petrov Galerkin (SUPG) stabilized virtual element method (VEM) for optimal control problem governed by a convection dominated diffusion equation is investigated. The virtual element discrete scheme is constructed based on the first-optimize-then-discretize strategy and SUPG stabilized virtual element approximation of the state equation and adjoint state equation. An a priori error estimate is derived for both the state, adjoint state, and the control. Numerical experiments are carried out to illustrate the theoretical findings.
Highlights
In this paper, we aim to discuss a priori error analysis of streamline upwind/Petrov Galerkin (SUPG) stabilized virtual element method (VEM) for the optimal control problem governed by the convection dominated diffusion equation
We aim to discuss a priori error analysis of SUPG stabilized virtual element method (VEM) for the optimal control problem governed by the convection dominated diffusion equation
By projection operators and the first-optimize--discretize strategy, we construct a computable SUPG-stabilized VEM discrete scheme for the optimal control problem governed by the convection dominated diffusion equation, where the control is implicitly discretized
Summary
We aim to discuss a priori error analysis of SUPG stabilized virtual element method (VEM) for the optimal control problem governed by the convection dominated diffusion equation.
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