ON THE SHARPNESS OF L(2)-ERROR ESTIMATES OF H-0(1)-PROJECTIONS ONTO SUBSPACES OF PIECEWISE, HIGH-ORDER POLYNOMIALS

In a plane polygonal domain, consider a Poisson problem -Delta u = f w ith homogeneous Dirichlet boundary condition and the p-version finite element solutions of this. We give various upper and fewer bounds for the error measured in L(2). In the case of a single element (i.e., a c onvex domain), we reduce the question of sharpness of these estimates to the behavior of a certain inf-sup constant, which is numerically de termined, and a likely sharp estimate is then conjectured. This is con firmed during a series of numerical experiments also for the case of a reentrant corner. For a one-dimensional analogue problem (of rotation al symmetry), sharp L(2)-error estimates are proven directly and via a n extension of the classical duality argument. Here, we give sharp L(i nfinity)-error estimates in some weighted and unweighted norms also.