Narrow Results

The choking flow phenomenon caused by local lateral contraction in open channels is studied in this paper. An equation for the determination of limit opening ratio is derived from the principles of conservation of energy and water continuity. The proposed equation takes into account for energy losses associated with local contraction and can accurately predict the limit opening ratios for choking.

Adaptive finite element methods (AFEM) are a fundamental numerical tool in science and engineering. They are known to outperform classical FEM in practice and deliver optimal convergence rates when the latter cannot. This paper surveys recent progress in the theory of AFEM which explains their success and provides a solid mathematical framework for further developments.

The paper surveys recent results on the finite element approximation of Hamilton-Jacobi-Bellman equations. Various methods are analyzed and error estimates in the maximum norm are derived. Also, a finite element monotone iterative scheme for the computation of the approximate solution is given and its geometrical convergence proved.