Large-scale floods are one of the major events that impact national economy and people’s livelihood every year during flood season. Predicting factors evolution is a worldwide problem. We use two-dimensional Saint-Venant equations as an example for high-performance computing in modelling behavior. Discretization with initial boundary conditions finite difference method explicit leapfrog scheme ...

In this work, we develop a robust adaptive well-balanced and positivity-preserving central-upwind scheme on unstructured triangular grids for shallow water equations. The numerical method is an extension of the from [{\sc Liu {\em et al.}},J. Comp. Phys, 374 (2018), pp. 213 - 236]. As part algorithm, obtain local posteriori error estimator efficient mesh refinement strategy. accuracy, high-reso...

In this paper, by using Schwarz rearrangement and isoperimetric inequalities, we prove comparison results for the solutions of Poisson equations on complete Riemannian manifolds with [Formula: see text], text] or which extends in [A. Alvino, C. Nitsch Trombetti, A Talenti result to elliptic problems Robin boundary conditions, Comm. Pure Appl. Math. 76(3) (2023) 585–603]. Furthermore, as applica...