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pro vyhledávání: '"Mascotto, L."'
We study the convergence analysis of a finite element method for the approximation of solutions to a seven-fields formulation of a magnetohydrodynamics model, which preserves the energy of the system, and the magnetic and cross helicities on the disc
Externí odkaz:
http://arxiv.org/abs/2407.19748
Autor:
Mascotto, L.
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 as an intro
Externí odkaz:
http://arxiv.org/abs/2304.10968
We prove stability bounds for Stokes-like virtual element spaces in two and three dimensions. Such bounds are also instrumental in deriving optimal interpolation estimates. Furthermore, we develop some numerical tests in order to investigate the beha
Externí odkaz:
http://arxiv.org/abs/2207.09844
We present two a posteriori error estimators for the virtual element method (VEM) based on global and local flux reconstruction in the spirit of [5]. The proposed error estimators are reliable and efficient for the $h$-, $p$-, and $hp$-versions of th
Externí odkaz:
http://arxiv.org/abs/2107.03716
We present a survey of the nonconforming Trefftz virtual element method for the Laplace and Helmholtz equations. For the latter, we present a new abstract analysis, based on weaker assumptions on the stabilization, and numerical results on the disper
Externí odkaz:
http://arxiv.org/abs/2102.11581
We present a low order virtual element discretization for time dependent Maxwell's equations, which allow for the use of general polyhedral meshes. Both the semi- and fully-discrete schemes are considered. We derive optimal a priori estimates and val
Externí odkaz:
http://arxiv.org/abs/2102.00950
Autor:
Artioli, E., Mascotto, L.
We construct a nonconforming virtual element method (ncVEM) based on approximation spaces that are enriched with special singular functions. This enriched ncVEM is tailored for the approximation of solutions to elliptic problems, which have singulari
Externí odkaz:
http://arxiv.org/abs/2005.02654
We discuss the $p$- and the $hp$-versions of the virtual element method for the approximation of eigenpairs of elliptic operators with a potential term on polygonal meshes. An application of this model is provided by the Schr\"odinger equation with a
Externí odkaz:
http://arxiv.org/abs/1812.09220
Akademický článek
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Autor:
Mascotto, L., Pichler, A.
We extend the nonconforming Trefftz virtual element method introduced in arXiv:1805.05634 to the case of the fluid-fluid interface problem, that is, a Helmholtz problem with piecewise constant wave number. With respect to the original approach, we ad
Externí odkaz:
http://arxiv.org/abs/1811.01645