$L^\infty$-Error Estimates on Graded Meshes with Application to Optimal Control

摘要: An $L^\infty$-error estimate of the finite element approximation an elliptic boundary value problem with Dirichlet conditions in domains corners is given. To achieve rate $h^2|\ln h|$ mesh has to be appropriately graded near interior angle larger than $\omega_0$, $\omega_0=\frac{\pi}{2}$ for Poisson problem. In contrast previous publications, norm function that approximated separated from constants this estimate. This result applied a linear-quadratic optimal control constraints on control. Two approaches are considered, one where by piecewise constant functions and improved postprocessing step, other not discretized. For both convergence maximum shown.