English

Stabilizer-free polygonal and polyhedral virtual elements

Numerical Analysis 2023-09-20 v1 Numerical Analysis

Abstract

Stabilizer-free PkP_k virtual elements are constructed on polygonal and polyhedral meshes. Here the interpolating space is the space of continuous PkP_k 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

R2 v1 2026-06-28T12:25:34.864Z