Solution Theory, Variational Formulations, and Functional a Posteriori Error Estimates for General First Order Systems with Applications to Electro-Magneto-Statics and More

DOI10.1080/01630563.2018.1490756zbMath1429.35048arXiv1611.02993OpenAlexW2949694278WikidataQ127760478 ScholiaQ127760478MaRDI QIDQ5205858

Dirk Pauly

Publication date: 17 December 2019

Published in: Numerical Functional Analysis and Optimization (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1611.02993

zbMATH Keywords

mixed boundary conditions

Mathematics Subject Classification ID

Error bounds for boundary value problems involving PDEs (65N15) Equations and inequalities involving linear operators, with vector unknowns (47A50) General (adjoints, conjugates, products, inverses, domains, ranges, etc.) (47A05) Electromagnetic theory (general) (78A25) Electro- and magnetostatics (78A30) First-order elliptic systems (35J46) Systems of linear first-order PDEs (35F35)

Related Items (10)

The index of some mixed order Dirac type operators and generalised Dirichlet-Neumann tensor fields ⋮ A compactness result for the div-curl system with inhomogeneous mixed boundary conditions for bounded Lipschitz domains and some applications ⋮ \textit{A posteriori} error estimates for hierarchical mixed-dimensional elliptic equations ⋮ Poincaré-Friedrichs type constants for operators involving grad, curl, and div: theory and numerical experiments ⋮ Hilbert complexes with mixed boundary conditions part 1: de Rham complex ⋮ Hilbert complexes with mixed boundary conditions—Part 2: Elasticity complex ⋮ Traces for Hilbert complexes ⋮ Low Frequency Asymptotics and Electro-Magneto-Statics for Time-Harmonic Maxwell's Equations in Exterior Weak Lipschitz Domains with Mixed Boundary Conditions ⋮ Functional a posteriori error estimates for boundary element methods ⋮ A short note on Helmholtz decompositions for bounded domains in $\mathbb{R}^3$

Cites Work

• Unnamed Item
• Accuracy verification methods. Theory and algorithms
• On Maxwell's and Poincaré's constants
• An elementary proof for a compact imbedding result in generalized electromagnetic theory
• On constants in Maxwell inequalities for bounded and convex domains
• A posteriori estimates for partial differential equations
• Zur Theorie der harmonischen Differentialformen
• Maxwell's boundary value problem on Riemannian manifolds with nonsmooth boundaries
• Two-sided a posteriori error bounds for electro-magnetostatic problems
• Time-Harmonic Maxwell Equations in the Exterior of Perfectly Conducting, Irregular Obstacles
• The Maxwell Compactness Property in Bounded Weak Lipschitz Domains with Mixed Boundary Conditions
• On the Maxwell constants in 3D
• Some decomposition theorems and their application to non-linear potential theory and Hodge theory
• On the boundary value problems of electro- and magnetostatics
• Randwertaufgaben in der verallgemeinerten Potentialtheorie
• A posteriori error estimation for variational problems with uniformly convex functionals

This page was built for publication: Solution Theory, Variational Formulations, and Functional a Posteriori Error Estimates for General First Order Systems with Applications to Electro-Magneto-Statics and More