Numerical investigation for a boundary optimal control of reaction-advection-diffusion equation using penalization technique

The objective of this paper is to describe the problem of boundary optimal control of the reaction-advection-diffusion equation for not very regular Dirichlet data and enumerate its qualitative properties. We check that the state equation is well-posed and we introduce the penalization technique to take into account the boundary condition of the Dirichlet type. Then, we consider the corresponding optimal boundary control problem and give the optimality conditions. Finally, we conducted a numerical investigation of the convergence of the solution of the penalized problem to the solution of the non-penalized one when the penalty parameter tends to zero in regular and non-regular domains.