DeepAI AI Chat
Log In Sign Up

SUPG-stabilized Virtual Elements for diffusion-convection problems: a robustness analysis

12/02/2020
by   L. Beirão da Veiga, et al.
0

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.

READ FULL TEXT
11/22/2021

A higher order nonconforming virtual element method for the Cahn-Hilliard equation

In this paper we develop a fully nonconforming virtual element method (V...
08/08/2022

A Stable Mimetic Finite-Difference Method for Convection-Dominated Diffusion Equations

Convection-diffusion equations arise in a variety of applications such a...
07/15/2021

A Petrov-Galerkin method for nonlocal convection-dominated diffusion problems

We present a Petrov-Gelerkin (PG) method for a class of nonlocal convect...
08/04/2020

A nonlinear weak constraint enforcement method for advection-dominated diffusion problems

We devise a stabilized method to weakly enforce bound constraints in the...
12/14/2022

On the maximum angle conditions for polyhedra with virtual element methods

Finite element methods are well-known to admit robust optimal convergenc...