A posteriori optimization of parameters in stabilized methods for convection–diffusion problems — Part II

Extensions of algorithms for computing optimal stabilization parameters in finite element methods for convection–diffusion equations are presented. These extensions reduce the dimension of the control space, in comparison to available methods, and thus address the long computing times of these methods. One method is proposed that considers only relevant mesh cells, another method that uses groups of mesh cells, and the combination of both methods is also studied. The incorporation of these methods within a gradient-based optimization procedure, via solving an adjoint problem, is explained. Numerical studies provide impressions on the gain of efficiency as well as on the loss of accuracy if control spaces with reduced dimensions are utilized.