Bounds on projections onto bivariate polynomial spline spaces with stable local bases (Q1601820)

In 1972, Carl de Boor stated his famous conjecture about the uniform boundedness of the \(L_2\)-spline projector, i.e. it should be uniformly bounded independently of the knot sequence. In this paper, the authors consider a special bivariate situation where the knot sequences are replaced by quasi-uniform triangulations. They establish the uniform boundedness in this case, where the bound only depends on the stability of the local spline basis, the polynomial degree and certain constants related to the quasi-uniformity of the triangulation.