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Title: The fully nonconforming virtual element method for biharmonic problems

Here in this paper, we address the numerical approximation of linear fourth-order elliptic problems on polygonal meshes. In particular, we present a novel nonconforming virtual element discretization of arbitrary order of accuracy for biharmonic problems. The approximation space is made of possibly discontinuous functions, thus giving rise to the fully nonconforming virtual element method. We derive optimal error estimates in a suitable (broken) energy norm and present numerical results to assess the validity of the theoretical estimates.
Authors:
 [1] ;  [2] ;  [1]
  1. Politecnico di Milano (Italy). MOX, Dipartimento di Matematica
  2. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Publication Date:
Report Number(s):
LA-UR-16-26955
Journal ID: ISSN 0218-2025
Grant/Contract Number:
89233218CNA000001; AC52-06NA25396; 2012HBLYE4; RBSI14VTOS
Type:
Accepted Manuscript
Journal Name:
Mathematical Models and Methods in Applied Sciences
Additional Journal Information:
Journal Volume: 28; Journal Issue: 02; Journal ID: ISSN 0218-2025
Publisher:
World Scientific
Research Org:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Org:
USDOE Laboratory Directed Research and Development (LDRD) Program; Ministry of Education, Universities and Research (MIUR)
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; Mathematics; Virtual Element Methods; Bi-harmonic problems; Nonconforming methods
OSTI Identifier:
1504646

Antonietti, Paola F., Manzini, Gianmarco, and Verani, Marco. The fully nonconforming virtual element method for biharmonic problems. United States: N. p., Web. doi:10.1142/S0218202518500100.
Antonietti, Paola F., Manzini, Gianmarco, & Verani, Marco. The fully nonconforming virtual element method for biharmonic problems. United States. doi:10.1142/S0218202518500100.
Antonietti, Paola F., Manzini, Gianmarco, and Verani, Marco. 2018. "The fully nonconforming virtual element method for biharmonic problems". United States. doi:10.1142/S0218202518500100. https://www.osti.gov/servlets/purl/1504646.
@article{osti_1504646,
title = {The fully nonconforming virtual element method for biharmonic problems},
author = {Antonietti, Paola F. and Manzini, Gianmarco and Verani, Marco},
abstractNote = {Here in this paper, we address the numerical approximation of linear fourth-order elliptic problems on polygonal meshes. In particular, we present a novel nonconforming virtual element discretization of arbitrary order of accuracy for biharmonic problems. The approximation space is made of possibly discontinuous functions, thus giving rise to the fully nonconforming virtual element method. We derive optimal error estimates in a suitable (broken) energy norm and present numerical results to assess the validity of the theoretical estimates.},
doi = {10.1142/S0218202518500100},
journal = {Mathematical Models and Methods in Applied Sciences},
number = 02,
volume = 28,
place = {United States},
year = {2018},
month = {2}
}