Journal
APPLIED NUMERICAL MATHEMATICS
Volume 143, Issue -, Pages 97-111Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/j.apnum.2019.04.002
Keywords
Nonconforming virtual element; Parabolic problem; Polygonal or polyhedral meshes
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Funding
- National Natural Science Foundation of China [11701522]
- Research Foundation for Advanced Talents of Henan University of Technology [2018BS013]
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The nonconforming virtual element method for the parabolic problem is developed in this paper, where the semi-discrete and fully discrete formulations are presented. In order to analyze the convergence of the method, we construct a projection operator in the sense of the energy norm and give the corresponding error estimates in the L-2 norm and broken H-1 semi-norm. With the help of the energy projection operator, we prove the optimal convergence of the nonconforming virtual element method in the semi-discrete and fully discrete formulations, respectively. Finally, we investigate the convergence of the nonconforming virtual element method by some numerical examples, which verify the theoretical results. (C) 2019 IMACS. Published by Elsevier B.V. All rights reserved.
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