We consider the solution of a second order elliptic PDE with inhomogeneous Dirichlet data by means of adaptive lowest-order FEM. As is usually done in practice, the given Dirichlet data are discretized by nodal interpolation. As model example serves the Poisson equation with mixed Dirichlet-Neumann boundary conditions. For error estimation, we use an edge-based residual error estimator which re...

We show how to construct stable quasi-interpolation schemes in the bivariate spline spaces S r d (4) with d 3r+2 which achieve optimal approximation order. In addition to treating the usual max norm, we also give results in the L p norms, and show that the methods also approximate derivatives to optimal order. We pay special attention to the approximation constants, and show that they depend on...

A weight function w(x) on (0, l) or (l,∞) , is said to be quasi-monotone if w(x)x−a0 C0w(y)y−a0 either for all x y or for all y x, for some a0 ∈ R , C0 1 . In this paper we discuss, complement and unify several results concerning quasi-monotone functions. In particular, some new results concerning the close connection to index numbers and generalized Bary-Stechkin classes are proved and applied...