2,376 research outputs found
The Virtual Element Method with curved edges
In this paper we initiate the investigation of Virtual Elements with curved
faces. We consider the case of a fixed curved boundary in two dimensions, as it
happens in the approximation of problems posed on a curved domain or with a
curved interface. While an approximation of the domain with polygons leads, for
degree of accuracy , to a sub-optimal rate of convergence, we show
(both theoretically and numerically) that the proposed curved VEM lead to an
optimal rate of convergence
Virtual Elements for the Navier-Stokes problem on polygonal meshes
A family of Virtual Element Methods for the 2D Navier-Stokes equations is
proposed and analysed. The schemes provide a discrete velocity field which is
point-wise divergence-free. A rigorous error analysis is developed, showing
that the methods are stable and optimally convergent. Several numerical tests
are presented, confirming the theoretical predictions. A comparison with some
mixed finite elements is also performed
Robust Finite Elements for linearized Magnetohydrodynamics
We introduce a pressure robust Finite Element Method for the linearized
Magnetohydrodynamics equations in three space dimensions, which is provably
quasi-robust also in the presence of high fluid and magnetic Reynolds numbers.
The proposed scheme uses a non-conforming BDM approach with suitable DG terms
for the fluid part, combined with an -conforming choice for the magnetic
fluxes. The method introduces also a specific CIP-type stabilization associated
to the coupling terms. Finally, the theoretical result are further validated by
numerical experiments
SUPG-stabilized Virtual Elements for diffusion-convection problems: a robustness analysis
The objective of this contribution is to develop a convergence analysis for
SUPG-stabilized Virtual Element Methods in diffusion-convection problems that
is robust also in the convection dominated regime. For the original method
introduced in [Benedetto et al, CMAME 2016] we are able to show an "almost
uniform" error bound (in the sense that the unique term that depends in an
unfavorable way on the parameters is damped by a higher order mesh-size
multiplicative factor). We also introduce a novel discretization of the
convection term that allows us to develop error estimates that are fully robust
in the convection dominated cases. We finally present some numerical result
Weak in Space, Log in Time Improvement of the Lady{\v{z}}enskaja-Prodi-Serrin Criteria
In this article we present a Lady{\v{z}}enskaja-Prodi-Serrin Criteria for
regularity of solutions for the Navier-Stokes equation in three dimensions
which incorporates weak norms in the space variables and log improvement
in the time variable.Comment: 14 pages, to appea
On the regularity up to the boundary for certain nonlinear elliptic systems
We consider a class of nonlinear elliptic systems and we prove regularity up to the boundary for second order derivatives. In the proof we trace carefully the dependence on the various parameters of the problem, in order to establish, in a further work, results for more general systems
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