Stabilizer-free polygonal and polyhedral virtual elements
Numerical Analysis
2023-09-20 v1 Numerical Analysis
Abstract
Stabilizer-free virtual elements are constructed on polygonal and polyhedral meshes. Here the interpolating space is the space of continuous polynomials on a triangular-subdivision of each polygon, or a tetrahedral-subdivision of each polyhedron. With such an accurate and proper interpolation, the stabilizer of the virtual elements is eliminated while the system is kept positive-definite. We show that the stabilizer-free virtual elements converge at the optimal order in 2D and 3D. Numerical examples are computed, validating the theory.
Cite
@article{arxiv.2309.10250,
title = {Stabilizer-free polygonal and polyhedral virtual elements},
author = {Yanping Lin and Mo Mu and Shangyou Zhang},
journal= {arXiv preprint arXiv:2309.10250},
year = {2023}
}
Comments
arXiv admin note: text overlap with arXiv:2309.09660