A Study on Anisotropic Mesh Adaptation for Finite Element Approximation of Eigenvalue Problems with Anisotropic Diffusion Operators
From MaRDI portal
Publication:3457831
DOI10.1137/140958554zbMath1329.65264arXiv1402.6001OpenAlexW2952125423MaRDI QIDQ3457831
Publication date: 18 December 2015
Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1402.6001
numerical examplesimage processingeigenvalue problemfinite elementerror analysiserror boundsLaplace-Beltrami operatormesh adaptationanisotropic diffusionanisotropic meshradiation hydrodynamics
Estimates of eigenvalues in context of PDEs (35P15) 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) Numerical methods for eigenvalue problems for boundary value problems involving PDEs (65N25)
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Adaptive moving mesh methods
- Sign-preserving of principal eigenfunctions in P1 finite element approximation of eigenvalue problems of second-order elliptic operators
- Convergence and optimal complexity of adaptive finite element eigenvalue computations
- A mixed implicit-explicit finite difference scheme for heat transport in magnetised plasmas
- Anisotropic interpolation with applications to the finite element method
- Interpolation remainder theory from Taylor expansions on triangles
- Anisotropic error estimates for elliptic problems
- Metric tensors for anisotropic mesh generation
- Variational mesh adaptation. II: Error estimates and monitor functions
- A new methodology for anisotropic mesh refinement based upon error gradients
- A new anisotropic mesh adaptation method based upon hierarchical a posteriori error estimates
- Preserving monotonicity in anisotropic diffusion
- Spectral stability of Dirichlet second order uniformly elliptic operators
- Unstructured grid optimization for improved monotonicity of discrete solutions of elliptic equations with highly anisotropic coefficients
- Eigenvalue approximation by the finite element method
- Error estimation and anisotropic mesh refinement for 3D laminar aerodynamic flow simulations
- Adaptive computation of smallest eigenvalues of self-adjoint elliptic partial differential equations
- Finite element approximation of eigenvalue problems
- Some Remarks on Eigenvalue Approximation by Finite Elements
- How a Nonconvergent Recovered Hessian Works in Mesh Adaptation
- On estimators for eigenvalue/eigenvector approximations
- Conditioning of finite element equations with arbitrary anisotropic meshes
- Optimal anisotropic meshes for minimizing interpolation errors in $L^p$-norm
- Computation of geometric partial differential equations and mean curvature flow
- On Optimal Interpolation Triangle Incidences
- A Convergent Adaptive Method for Elliptic Eigenvalue Problems
- Discontinuous Galerkin Methods for Advection-Diffusion-Reaction Problems on Anisotropically Refined Meshes
- Enhancing eigenvalue approximation by gradient recovery on adaptive meshes
- A posteriorierror estimation and anisotropy detection with the dual-weighted residual method
- Finite Element-Galerkin Approximation of the Eigenvalues and Eigenvectors of Selfadjoint Problems
- Image Selective Smoothing and Edge Detection by Nonlinear Diffusion
- Image Selective Smoothing and Edge Detection by Nonlinear Diffusion. II
- Discretization on Unstructured Grids for Inhomogeneous, Anisotropic Media. Part I: Derivation of the Methods
- Discretization on Unstructured Grids For Inhomogeneous, Anisotropic Media. Part II: Discussion And Numerical Results
- Analysis of total variation flow and its finite element approximations
- An Anisotropic Error Indicator Based on Zienkiewicz--Zhu Error Estimator: Application to Elliptic and Parabolic Problems
- A Posteriori and a Priori Error Analysis for Finite Element Approximations of Self-Adjoint Elliptic Eigenvalue Problems
- A two-grid discretization scheme for eigenvalue problems
- Stability of Explicit Runge-Kutta Methods for High Order Finite Element Approximation of Linear Parabolic Equations
- Finite element methods for surface PDEs
- An interpolation error estimate in $\mathcal{R}^2$ based on the anisotropic measures of higher order derivatives
- A Study on the Conditioning of Finite Element Equations with Arbitrary Anisotropic Meshes http://admin.global-sci.org/api/check/checkTitleUpper?page=1&cate_id=13ia a Density Function Approach
- Rayleigh-Ritz Approximation by Piecewise Cubic Polynomials
- New anisotropic a priori estimates
- A posteriori error control for finite element approximations of elliptic eigenvalue problems
- Robust a posteriori error estimation for a singularly perturbed reaction--diffusion equation on anisotropic tetrahedral meshes
