7 research outputs found
p- and hp- virtual elements for the Stokes problem
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
velocities. This allows us to re-interpret the standard VEM for Stokes as a
VEM, where the test and trial discrete velocities are sought in Poisson-like VE
spaces. The upside of this fact is that we inherit from [7] an explicit
analysis of best interpolation results in VE spaces, as well as stabilization
estimates that are explicit in terms of the degree of accuracy of the method.
We prove exponential convergence of the hp-VEM for Stokes problems with regular
right-hand sides. We corroborate the theoretical estimates with numerical tests
for both the p- and hp-versions of the method
The Virtual Element Method for the 3D Resistive Magnetohydrodynamic model
We present a four-field Virtual Element discretization for the time-dependent
resistive Magnetohydrodynamics equations in three space dimensions, focusing on
the semi-discrete formulation. The proposed method employs general polyhedral
meshes and guarantees velocity and magnetic fields that are divergence free up
to machine precision. We provide a full convergence analysis under suitable
regularity assumptions, which is validated by some numerical tests
A Hybrid High-Order method for incompressible flows of non-Newtonian fluids with power-like convective behaviour
In this work, we design and analyze a Hybrid High-Order (HHO) discretization
method for incompressible flows of non-Newtonian fluids with power-like
convective behaviour. We work under general assumptions on the viscosity and
convection laws, that are associated with possibly different Sobolev exponents
r > 1 and s > 1. After providing a novel weak formulation of the continuous
problem, we study its well-posedness highlighting how a subtle interplay
between the exponents r and s determines the existence and uniqueness of a
solution. We next design an HHO scheme based on this weak formulation and
perform a comprehensive stability and convergence analysis, including
convergence for general data and error estimates for shear-thinning fluids and
small data. The HHO scheme is validated on a complete panel of model problems.Comment: 33 pages, 3 figures, 3 table