Anisotropic a posteriori error estimate for the Virtual Element Method

01/02/2020
by   Paola Francesca Antonietti, et al.
0

We derive an anisotropic a posteriori error estimate for the adaptive conforming Virtual Element approximation of a paradigmatic two-dimensional elliptic problem. In particular, we introduce a quasi-interpolant operator and exploit its approximation results to prove the reliability of the error indicator. We design and implement the corresponding adaptive polygonal anisotropic algorithm. Several numerical tests assess the superiority of the proposed algorithm in comparison with standard polygonal isotropic mesh refinement schemes.

READ FULL TEXT
POST COMMENT

Comments

There are no comments yet.

Authors

page 20

page 21

page 22

page 23

page 24

page 25

page 26

page 27

09/03/2020

An adaptive high-order unfitted finite element method for elliptic interface problems

We design an adaptive unfitted finite element method on the Cartesian me...
01/21/2021

A priori and a posteriori error analysis of the lowest-order NCVEM for second-order linear indefinite elliptic problems

The nonconforming virtual element method (NCVEM) for the approximation o...
01/16/2020

An adaptive finite element DtN method for the three-dimensional acoustic scattering problem

This paper is concerned with a numerical solution of the acoustic scatte...
04/23/2020

Adaptive virtual element methods with equilibrated flux

We present an hp-adaptive virtual element method (VEM) based on the hype...
01/23/2017

An hp-adaptive strategy for elliptic problems

In this paper a new hp-adaptive strategy for elliptic problems based on ...
05/12/2020

Adaptive non-hierarchical Galerkin methods for parabolic problems with application to moving mesh and virtual element methods

We present a posteriori error estimates for inconsistent and non-hierarc...
03/27/2019

Posteriori Probabilistic Bounds of Convex Scenario Programs with Validation Tests

Scenario programs have established themselves as efficient tools towards...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.