The efficiency of a nudging data assimilation algorithm using higher order finite element interpolating operators is studied. Numerical experiments are presented for the 2D Navier–Stokes equations in three cases: shear flow an annulus, forced disk with off-center cavity, and box all satisfying Dirichlet boundary conditions. In cases, second interpolation coarse-grain shown to outperform first i...

In this paper, we introduce a new Virtual Element Method (VEM) not requiring any stabilization term based on the usual enhanced first-order VEM space. The method relies modified formulation of discrete diffusion operator that ensures stability preserving all properties differential operator.

The Largest Empty Circle problem seeks the largest circle centered within the convex hull of a set P of n points in R2 and devoid of points from P . In this paper, we introduce a query version of this well-studied problem. In our query version, we are required to preprocess P so that when given a query line Q, we can quickly compute the largest empty circle centered at some point on Q and withi...