Related papers: Stability and interpolation properties for Stokes-…
We prove stability and interpolation estimates for Hellinger-Reissner virtual elements; the constants appearing in such estimates only depend on the aspect ratio of the polytope under consideration and the degree of accuracy of the scheme.…
The virtual element method was introduced 10 years ago and it has generated a large number of theoretical results and applications ever since. Here, we overview the main mathematical results concerning the stabilization term of the method…
We develop interpolation error estimates for general order standard and serendipity edge and face virtual elements in two and three dimensions. Contextually, we investigate the stability properties of the associated L2 discrete bilinear…
We analyse the interpolation properties of 2D and 3D low order virtual element face and edge spaces, which generalize N\'ed\'elec and Raviart-Thomas polynomials to polygonal-polyhedral meshes. Moreover, we investigate the stability…
In this paper, we propose a new virtual interpolation point method to formulate the discrete Stokes equations. We form virtual staggered structure for the velocity and pressure from the actual computation node set. The virtual interpolation…
The paper shows an inf-sup stability property for several well-known 2D and 3D Stokes elements on triangulations which are not fitted to a given smooth or polygonal domain. The property implies stability and optimal error estimates for a…
We analyse the p- and hp-versions of the virtual element method (VEM) for the the Stokes problem on a polygonal domain. The key tool in the analysis is the existence of a bijection between Poisson-like and Stokes-like VE spaces for the…
The present paper has two objectives. On one side, we develop and test numerically divergence free Virtual Elements in three dimensions, for variable ``polynomial'' order. These are the natural extension of the two-dimensional divergence…
A stability of nearly limiting Stokes waves to superharmonic perturbations is considered numerically. The new, previously inaccessible branches of superharmonic instability were investigated. Our numerical simulations suggest that…
We investigate stability of Fredholm properties on interpolation scales of quasi-Banach spaces. This analysis is motivated by problems arising in PDE's and several applications are presented.
We show that, on convex polytopes and two or three dimensions, the finite element Stokes projection is stable on weighted spaces $\mathbf{W}^{1,p}_0(\omega,\Omega) \times L^p(\omega,\Omega)$, where the weight belongs to a certain…
This paper concerns the instability and stability of the trivial steady states of the incompressible Navier-Stokes equations with Navier-slip boundary conditions in a slab domain in dimension two. The main results show that the stability…
We introduce remarkable upper bounds for the interpolation error constants on triangles, which are sharp and given by simple formulas. These constants are crucial in analyzing interpolation errors, particularly those associated with the…
We consider the inverse problem of the detection of a single body, immersed in a bounded container filled with a fluid which obeys the Stokes equations, from a single measurement of force and velocity on a portion of the boundary. We obtain…
Block-to-block interface interpolation operators are constructed for several common high-order finite difference discretizations. In contrast to conventional interpolation operators, these new interpolation operators maintain the strict…
The stability radius for finitely many interconnected linear exponentially stable well-posed systems with respect to static perturbations is studied. If the output space of each system is finite-dimensional, then a lower bound for the…
The paper addresses stability and finite element analysis of the stationary two-phase Stokes problem with a piecewise constant viscosity coefficient experiencing a jump across the interface between two fluid phases. We first prove a priori…
We review recent stability and separation results in volume comparison problems and use them to prove several hyper- plane inequalities for intersection and projection bodies.
This article presents a higher-order spectral element method for the two-dimensional Stokes interface problem involving a piecewise constant viscosity coefficient. The proposed numerical formulation is based on least-squares formulation.…
A lower bound for the interleaving distance on persistence vector spaces is given in terms of rank invariants. This offers an alternative proof of the stability of rank invariants.