On eigenmode approximation for Dirac equations: Differential forms and fractional Sobolev spaces

DOI10.1090/mcom/3233zbMath1380.65350arXiv1511.06272OpenAlexW2964236849MaRDI QIDQ4600700

Snorre H. Christiansen

Publication date: 12 January 2018

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1511.06272

zbMATH Keywords

convergencefinite elementseigenmodedifferential formsDirac equationfractional Sobolev spacesmollified interpolator

Mathematics Subject Classification ID

Estimates of eigenvalues in context of PDEs (35P15) Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) 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) PDEs in connection with quantum mechanics (35Q40) Numerical methods for eigenvalue problems for boundary value problems involving PDEs (65N25)

Related Items (2)

Poincaré-Friedrichs type constants for operators involving grad, curl, and div: theory and numerical experiments ⋮ First-Kind Boundary Integral Equations for the Dirac Operator in 3-Dimensional Lipschitz Domains

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• On the equivalence of fractional-order Sobolev semi-norms
• On the linearization of Regge calculus
• Real interpolation of spaces of differential forms
• On the div-curl lemma in a Galerkin setting
• An introduction to Sobolev spaces and interpolation spaces
• Estimation of the effect of numerical integration in finite element eigenvalue approximation
• The electric field integral equation on Lipschitz screens: definitions and numerical approximation
• Partial differential equations. 1: Basic theory
• Minimal mixed finite elements on polyhedra
• Un teorema di interpolazione; applicazioni ai problemi ai limiti per l er le equazioni differenziali a derivate parziali
• Stability of Hodge decompositions in finite element spaces of differential forms in arbitrary dimension
• On high order finite element spaces of differential forms
• Constructions of some minimal finite element systems
• Convergence of a constrained finite element discretization of the Maxwell Klein Gordon equation
• GRADIENT SCHEMES: A GENERIC FRAMEWORK FOR THE DISCRETISATION OF LINEAR, NONLINEAR AND NONLOCAL ELLIPTIC AND PARABOLIC EQUATIONS
• Commuting diagrams for the TNT elements on cubes
• Finite element approximation of eigenvalue problems
• Topics in structure-preserving discretization
• Finite elements in computational electromagnetism
• Finite element exterior calculus, homological techniques, and applications
• A CONSTRUCTION OF SPACES OF COMPATIBLE DIFFERENTIAL FORMS ON CELLULAR COMPLEXES
• Finite element exterior calculus: from Hodge theory to numerical stability
• Spectral pollution and how to avoid it
• Foundations of Finite Element Methods for Wave Equations of Maxwell Type
• Finite Element-Galerkin Approximation of the Eigenvalues and Eigenvectors of Selfadjoint Problems
• Corrigendum: Finite Element-Galerkin Approximation of the Eigenvalues and Eigenvectors of Selfadjoint Problems
• Discrete Fredholm properties and convergence estimates for the electric field integral equation
• On variational eigenvalue approximation of semidefinite operators
• Finite element differential forms on cubical meshes
• The Mathematical Theory of Finite Element Methods
• A posteriori error estimates for Maxwell equations
• Smoothed projections in finite element exterior calculus
• Remarks on the Discretization of Some Noncoercive Operator with Applications to Heterogeneous Maxwell Equations

This page was built for publication: On eigenmode approximation for Dirac equations: Differential forms and fractional Sobolev spaces