Modified heuristic criterion for parameter choice for one stabilization scheme of the finite element method

We consider a modi cation to a heuristic criterion for the optimal choice of the stabilization parameter in a certain nite element scheme for the singularly perturbed di usion-advectionreaction problem. This criterion is based on a minimization problem of the function of the stabilization parameter and the corresponding algorithm for nding the minimum. The function generally exhibits two extremum points: a local minimum and a local maximum. This forces the algorithm to repeatedly use an additional controlled heuristic "try-and-check" procedure, which can be ine cient in some cases. In this article, we propose simple heuristic modi cations to the criterion to eliminate the second maximum point, making ordinary bisection method applicable to the minimum- nding procedure.