The Mixed Virtual Element Method on curved edges in two dimensions
Numerical Analysis
2021-09-01 v1 Numerical Analysis
Abstract
In this work, we propose an extension of the mixed Virtual Element Method (VEM) for bi-dimensional computational grids with curvilinear edge elements. The approximation by means of rectilinear edges of a domain with curvilinear geometrical feature, such as a portion of domain boundary or an internal interface, may introduce a geometrical error that degrades the expected order of convergence of the scheme. In the present work a suitable VEM approximation space is proposed to consistently handle curvilinear geometrical objects, thus recovering optimal convergence rates. The resulting numerical scheme is presented along with its theoretical analysis and several numerical test cases to validate the proposed approach.
Cite
@article{arxiv.2007.13513,
title = {The Mixed Virtual Element Method on curved edges in two dimensions},
author = {Franco Dassi and Alessio Fumagalli and Davide Losapio and Stefano Scialò and Anna Scotti and Giuseppe Vacca},
journal= {arXiv preprint arXiv:2007.13513},
year = {2021}
}