Convergence and quasi-optimality of adaptive finite element methods for harmonic forms

DOI10.1007/s00211-016-0862-6zbMath1378.65177arXiv1605.08813OpenAlexW2963458162MaRDI QIDQ2407466

Alan Demlow

Publication date: 29 September 2017

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1605.08813

zbMATH Keywords

convergenceelliptic eigenvalue problemharmonic formsquasi-optimalityadaptive finite element

Mathematics Subject Classification ID

Estimates of eigenvalues in context of PDEs (35P15) Error bounds for boundary value problems involving PDEs (65N15) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Numerical methods for eigenvalue problems for boundary value problems involving PDEs (65N25)

Related Items (7)

An extended Galerkin analysis in finite element exterior calculus ⋮ Convergence of Adaptive Mixed Finite Element Methods for the Hodge Laplacian Equation: Without Harmonic Forms ⋮ Computational Homogenization of Time-Harmonic Maxwell's Equations ⋮ Adaptive Finite Element Method for the Maxwell Eigenvalue Problem ⋮ Quasi-optimal adaptive mixed finite element methods for controlling natural norm errors ⋮ Some Convergence and Optimality Results of Adaptive Mixed Methods in Finite Element Exterior Calculus ⋮ Adaptive Mixed Finite Element Methods for Non-self-adjoint Indefinite Second-Order Elliptic PDEs with Optimal Rates

Uses Software

• iFEM

Cites Work

• A posteriori error estimates for finite element exterior calculus: the de Rham complex
• Automatic generation of cuts on large-sized meshes for the \(T-\Omega \) geometric eddy-current formulation
• Convergence and optimal complexity of adaptive finite element eigenvalue computations
• Eddy current approximation of Maxwell equations. Theory, algorithms and applications
• Convergence rates of AFEM with \(H^{-1}\) data
• The topology of Helmholtz domains
• Singularities of electromagnetic fields in polyhedral domains
• An optimal adaptive FEM for eigenvalue clusters
• The regularity of the Stokes operator and the Fujita-Kato approach to the Navier-Stokes initial value problem in Lipschitz domains
• Optimality of a standard adaptive finite element method
• Optimal control of low-frequency electromagnetic fields in multiply connected conductors
• Construction of a Finite Element Basis of the First de Rham Cohomology Group and Numerical Solution of 3D Magnetostatic Problems
• Generators of $H_1(\Gamma_{h},\mathbbZ)$ for Triangulated Surfaces: Construction and Classification
• Convergence and Optimality of Higher-Order Adaptive Finite Element Methods for Eigenvalue Clusters
• Local bounded cochain projections
• Convergence and Optimality of Adaptive Mixed Methods for Poisson's Equation in the FEEC Framework
• Finite elements in computational electromagnetism
• Finite element exterior calculus, homological techniques, and applications
• Convergence and quasi-optimal complexity of adaptive finite element computations for multiple eigenvalues
• Finite Element Interpolation of Nonsmooth Functions Satisfying Boundary Conditions
• Finite element exterior calculus: from Hodge theory to numerical stability
• A Convergent Adaptive Method for Elliptic Eigenvalue Problems
• CONVERGENCE OF ADAPTIVE FINITE ELEMENT METHODS FOR EIGENVALUE PROBLEMS
• Quasi-Optimal Convergence Rate for an Adaptive Finite Element Method
• Nodal Auxiliary Space Preconditioning in H(curl) and H(div) Spaces
• Convergence and optimality of adaptive edge finite element methods for time-harmonic Maxwell equations
• The completion of locally refined simplicial partitions created by bisection
• A posteriori error estimates for Maxwell equations
• Smoothed projections in finite element exterior calculus

This page was built for publication: Convergence and quasi-optimality of adaptive finite element methods for harmonic forms