572 research outputs found
Global regularity properties of steady shear thinning flows
In this paper we study the regularity of weak solutions to systems of
p-Stokes type, describing the motion of some shear thinning fluids in certain
steady regimes. In particular we address the problem of regularity up to the
boundary improving previous results especially in terms of the allowed range
for the parameter p
The well-posedness issue for an inviscid zero-Mach number system in general Besov spaces
The present paper is devoted to the study of a zero-Mach number system with
heat conduction but no viscosity. We work in the framework of general
non-homogeneous Besov spaces , with and
for any , which can be embedded into the class of globally Lipschitz
functions.
We prove a local in time well-posedness result in these classes for general
initial densities and velocity fields. Moreover, we are able to show a
continuation criterion and a lower bound for the lifespan of the solutions.
The proof of the results relies on Littlewood-Paley decomposition and
paradifferential calculus, and on refined commutator estimates in Chemin-Lerner
spaces.Comment: This submission supersedes the first part of arXiv:1305.113
A Virtual Element Method for elastic and inelastic problems on polytope meshes
We present a Virtual Element Method (VEM) for possibly nonlinear elastic and
inelastic problems, mainly focusing on a small deformation regime. The
numerical scheme is based on a low-order approximation of the displacement
field, as well as a suitable treatment of the displacement gradient. The
proposed method allows for general polygonal and polyhedral meshes, it is
efficient in terms of number of applications of the constitutive law, and it
can make use of any standard black-box constitutive law algorithm. Some
theoretical results have been developed for the elastic case. Several numerical
results within the 2D setting are presented, and a brief discussion on the
extension to large deformation problems is included
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
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