Optical Monitors and OT/GRB analyses

The Optical Monitors, despite of lower detection limits, are still valuable for detection of prompt real-time and (hypothetical) pre-burst optical emission of gamma-ray bursts. We refer on the ongoing project at the Astronomical Institute in Ondrejov based on digitized data from the photographic EN network

On the worst scenario method: Application to a quasilinear elliptic 2D-problem with uncertain coefficients

summary:We apply a theoretical framework for solving a class of worst scenario problems to a problem with a nonlinear partial differential equation. In contrast to the one-dimensional problem investigated by P. Harasim in Appl. Math. 53 (2008), No. 6, 583–598, the two-dimensional problem requires stronger assumptions restricting the admissible set to ensure the monotonicity of the nonlinear operator in the examined state problem, and, as a result, to show the existence and uniqueness of the state solution. The existence of the worst scenario is proved through the convergence of a sequence of approximate worst scenarios. Furthermore, it is shown that the Galerkin approximation of the state solution can be calculated by means of the Kachanov method as the limit of a sequence of solutions to linearized problems

Superconvergence of The Derivative Patch Recovery Technique and A Posteriori Error Estimation

The derivative patch recovery technique developed by Zienkiewicz and Zhu [1] - [3] for the finite element method is analyzed. It is shown that, for one dimensional problems and two dimensional problems using tensor product elements, the patch recovery technique yields superconvergence recovery for the derivatives. Consequently, the error estimator based on the recovered derivative is asymptotically exact