On projection operators for numerical stabilization

Constructing the operators of projection onto appropriate linear manifolds is a very important problem for numerical stabilization of solutions to partial differential equations with the help of boundary feedback control. Two ways of projection resulting in continuous and discontinuous images for fixed smooth original functions are studied. Spectral characteristics of condition numbers for discrete projection operators are analyzed and compared. Optimization of these characteristics is discussed. Numerical results devoted to stabilization of solutions to Chafee-Infante's equations with initial functions obtained on the basis of both approaches are presented.