A Posteriori Error Estimates for the Laplace--Beltrami Operator on Parametric $C^2$ Surfaces

DOI10.1137/18M1169278zbMath1416.65414arXiv1802.01625OpenAlexW2963139439MaRDI QIDQ4633957

Alan Demlow, Andrea Bonito

Publication date: 7 May 2019

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

Full work available at URL: https://arxiv.org/abs/1802.01625

zbMATH Keywords

Laplace-Beltrami operatora posteriori error estimatesadaptive finite element methodssurface finite element methods

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) Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs (65N50)

Related Items (1)

Approximation of the Spectral Fractional Powers of the Laplace-Beltrami Operator

Uses Software

• deal.ii

Cites Work

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• Finite element methods for director fields on flexible surfaces
• High-order AFEM for the Laplace-Beltrami operator: convergence rates
• A finite element method for surface diffusion: the parametric case.
• An algorithm for evolutionary surfaces
• Computational parametric Willmore flow
• Parametric FEM for geometric biomembranes
• Elliptic boundary value problems on corner domains. Smoothness and asymptotics of solutions
• Error estimates for a semi-implicit fully discrete element scheme for the mean curvature flow of graphs
• Error analysis of a finite element method for the Willmore flow of graphs
• An algorithm for the elastic flow of surfaces
• Adaptive discontinuous Galerkin methods on surfaces
• Computational Parametric Willmore Flow with Spontaneous Curvature and Area Difference Elasticity Effects
• AFEM for Geometric PDE: The Laplace-Beltrami Operator
• Convergence analysis of variational and non-variational multigrid algorithms for the Laplace-Beltrami operator
• An Adaptive Surface Finite Element Method Based on Volume Meshes
• L₂and pointwise a posteriori error estimates for FEM for elliptic PDEs on surfaces
• Finite element approximation for the dynamics of asymmetric fluidic biomembranes
• Analysis of Highly Accurate Finite Element Based Algorithms for Computing Distances to Level Sets
• Dynamics of Biomembranes: Effect of the Bulk Fluid
• AFEM for the Laplace-Beltrami operator on graphs: Design and conditional contraction property
• deal.II—A general-purpose object-oriented finite element library
• A finite element scheme for the evolution of orientational order in fluid membranes
• Higher-Order Finite Element Methods and Pointwise Error Estimates for Elliptic Problems on Surfaces
• Surface Diffusion of Graphs: Variational Formulation, Error Analysis, and Simulation
• Stable variational approximations of boundary value problems for Willmore flow with Gaussian curvature
• Some mathematical challenges in materials science
• Discrete anisotropic curvature flow of graphs
• Parametric Approximation of Willmore Flow and Related Geometric Evolution Equations
• An Adaptive Finite Element Method for the Laplace–Beltrami Operator on Implicitly Defined Surfaces
• Fully Discrete Finite Element Approximation for Anisotropic Surface Diffusion of Graphs
• Finite element discretization of the Navier-Stokes equations with a free capillary surface

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