Discrete Hessian complexes in three dimensions
Long Chen, Xuehai Huang
TL;DR
This paper introduces a new family of conforming virtual element Hessian complexes on tetrahedral meshes, which are used to discretize the Einstein-Bianchi system with optimal convergence rates.
Contribution
It constructs conforming virtual element Hessian complexes in three dimensions based on polynomial tensor space decompositions, enabling improved discretization of complex systems.
Findings
Achieved optimal order convergence in discretizing the Einstein-Bianchi system
Developed a new virtual element Hessian complex construction for tetrahedral meshes
Demonstrated the effectiveness of the complexes in numerical experiments
Abstract
A family of conforming virtual element Hessian complexes on tetrahedral meshes are constructed based on decompositions of polynomial tensor spaces. They are applied to discretize the linearized time-independent Einstein-Bianchi system with optimal order convergence.
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Taxonomy
TopicsBlack Holes and Theoretical Physics · Advanced Numerical Methods in Computational Mathematics · Quantum chaos and dynamical systems