152,818 research outputs found
Some Error Analysis on Virtual Element Methods
Some error analysis on virtual element methods including inverse
inequalities, norm equivalence, and interpolation error estimates are presented
for polygonal meshes which admits a virtual quasi-uniform triangulation
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
A Virtual Element Method for a Nonlocal FitzHugh-Nagumo Model of Cardiac Electrophysiology
We present a Virtual Element Method (VEM) for a nonlocal reaction-diffusion
system of the cardiac electric field. To this system, we analyze an
-conforming discretization by means of VEM which can make use of
general polygonal meshes. Under standard assumptions on the computational
domain, we establish the convergence of the discrete solution by considering a
series of a priori estimates and by using a general compactness
criterion. Moreover, we obtain optimal order space-time error estimates in the
norm. Finally, we report some numerical tests supporting the theoretical
results
Virtual Element Methods on Meshes with Small Edges or Faces
We consider a model Poisson problem in () and establish error
estimates for virtual element methods on polygonal or polyhedral meshes that
can contain small edges () or small faces ().Comment: 36 page
The nonconforming virtual element method for eigenvalue problems
We analyse the nonconforming Virtual Element Method (VEM) for the
approximation of elliptic eigenvalue problems. The nonconforming VEM allow to
treat in the same formulation the two- and three-dimensional case.We present
two possible formulations of the discrete problem, derived respectively by the
nonstabilized and stabilized approximation of the L^2-inner product, and we
study the convergence properties of the corresponding discrete eigenvalue
problem. The proposed schemes provide a correct approximation of the spectrum,
in particular we prove optimal-order error estimates for the eigenfunctions and
the usual double order of convergence of the eigenvalues. Finally we show a
large set of numerical tests supporting the theoretical results, including a
comparison with the conforming Virtual Element choice
Virtual Element Method for fourth order problems: estimates
We analyse the family of -Virtual Elements introduced in
\cite{Brezzi:Marini:plates} for fourth-order problems and prove optimal
estimates in and in via classical duality arguments
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