High-Order Approximation of Gaussian Curvature with Regge Finite Elements

DOI10.1137/19M1255549zbMath1447.65139arXiv1905.07004WikidataQ114074257 ScholiaQ114074257MaRDI QIDQ5113131

Evan S. Gawlik

Publication date: 10 June 2020

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1905.07004

zbMATH Keywords

Riemannian metricscalar curvatureRicci scalarRegge calculusGaussian curvatureangle defectHellan-Herrmann-JohnsonRegge finite element

Mathematics Subject Classification ID

Error bounds for boundary value problems involving PDEs (65N15) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Numerical aspects of computer graphics, image analysis, and computational geometry (65D18) Lattice gravity, Regge calculus and other discrete methods in general relativity and gravitational theory (83C27)

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Cites Work

• Unnamed Item
• Unnamed Item
• Numerical Ricci-DeTurck flow
• Discrete conformal variations and scalar curvature on piecewise flat two- and three-dimensional manifolds
• On the linearization of Regge calculus
• Finite element approximations to surfaces of prescribed variable mean curvature
• On the convergence of metric and geometric properties of polyhedral surfaces
• Deformations of the scalar curvature
• Combinatorial Ricci flows on surfaces.
• Theory and practice of finite elements.
• On the curvature of piecewise flat spaces
• A convergent evolving finite element algorithm for mean curvature flow of closed surfaces
• On the angular defect of triangulations and the pointwise approximation of curvatures
• Convergence analysis of a discretization scheme for Gaussian curvature over triangular surfaces
• Isoparametric finite element approximation of Ricci curvature
• The simplicial Ricci tensor
• Finite Element Interpolation of Nonsmooth Functions Satisfying Boundary Conditions
• Curvatures of Smooth and Discrete Surfaces
• Mixed and nonconforming finite element methods : implementation, postprocessing and error estimates
• Analysis of Mixed Methods Using Mesh Dependent Norms
• Surface Diffusion of Graphs: Variational Formulation, Error Analysis, and Simulation
• An equilibration-based a posteriori error bound for the biharmonic equation and two finite element methods
• A two-energies principle for the biharmonic equation and ana posteriorierror estimator for an interior penalty discontinuous Galerkin approximation