Polynomial bounds for the solutions of parametric transmission problems on smooth, bounded domains

DOI10.1051/M2AN/2024057MaRDI QIDQ6667322

Victor Nistor, Hassan Mohsen, Simon Labrunie

Publication date: 20 January 2025

Published in: European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis (Search for Journal in Brave)

zbMATH Keywords

Sobolev spacesfinite element methodPoincaré inequalitytransmission problemsuncertainty quantificationstrongly elliptic operatorsparametric elliptic equations

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Singular elliptic equations (35J75)

Cites Work

• Title not available (Why is that?)
• Title not available (Why is that?)
• Title not available (Why is that?)
• Title not available (Why is that?)
• Title not available (Why is that?)
• Title not available (Why is that?)
• Title not available (Why is that?)
• Title not available (Why is that?)
• Title not available (Why is that?)
• Limiting absorption principle and well-posedness for the Helmholtz equation with sign changing coefficients
• Breaking the curse of dimensionality in sparse polynomial approximation of parametric PDEs
• Analysis of the finite element method for transmission/mixed boundary value problems on general polygonal domains
• Two- and three-field formulations for wave transmission between media with opposite sign dielectric constants
• Partial differential equations. II: Qualitative studies of linear equations
• Functional analysis, Sobolev spaces and partial differential equations
• A direct boundary integral equation method for transmission problems
• Direct and inverse error estimates for finite elements with mesh refinements
• Elliptic boundary value problems on corner domains. Smoothness and asymptotics of solutions
• Boundary layer methods for Lipschitz domains in Riemannian manifolds
• Anisotropic regularity results for Laplace and Maxwell operators in a polyhedron.
• Representations of Gaussian random fields and approximation of elliptic PDEs with lognormal coefficients
• Partial differential equations. 1: Basic theory
• Layer potentials \(C^*\)-algebras of domains with conical points
• \(T\)-coercivity and continuous Galerkin methods: application to transmission problems with sign changing coefficients
• Limiting absorption principle and well-posedness for the time-harmonic Maxwell equations with anisotropic sign-changing coefficients
• {\(T\)}-coercivity for scalar interface problems between dielectrics and metamaterials
• Uniform Shift Estimates for Transmission Problems and Optimal Rates of Convergence for the Parametric Finite Element Method
• Sobolev spaces on Riemannian manifolds with bounded geometry: General coordinates and traces
• T-Coercivity for the Maxwell Problem with Sign-Changing Coefficients
• ANALYTIC REGULARITY FOR LINEAR ELLIPTIC SYSTEMS IN POLYGONS AND POLYHEDRA
• Introduction to Uncertainty Quantification
• ANALYTIC REGULARITY AND POLYNOMIAL APPROXIMATION OF PARAMETRIC AND STOCHASTIC ELLIPTIC PDE'S
• Regularity of the solutions for elliptic problems on nonsmooth domains in ℝ³, Part I: countably normed spaces on polyhedral domains
• Spectral Methods for Uncertainty Quantification
• Characterizations of Function Spaces on a Complete RIEMANNian Manifold with Bounded Geometry
• Boundary Integral Operators on Lipschitz Domains: Elementary Results
• Analyse spectrale et singularités d'un problème de transmission non coercif
• General interface problems—I
• General interface problems—II
• Mathematical Analysis of Conducting and Superconducting Transmission Lines
• Differential operators on domains with conical points: precise uniform regularity estimates
• Galerkin Finite Element Approximations of Stochastic Elliptic Partial Differential Equations
• A Nonconforming Generalized Finite Element Method for Transmission Problems
• Quasi-Monte Carlo Bayesian estimation under Besov priors in elliptic inverse problems
• Gluing action groupoids: Fredholm conditions and layer potentials
• Well‐posedness of the Laplacian on manifolds with boundary and bounded geometry
• Improving the Rate of Convergence of High-Order Finite Elements on Polyhedra II: Mesh Refinements and Interpolation
• Fully Discrete Approximation of Parametric and Stochastic Elliptic PDEs
• Sobolev spaces on manifolds
• Boundary Integral Equations
• Near-optimal approximation methods for elliptic PDEs with lognormal coefficients
• A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data
• Polynomial estimates for solutions of parametric elliptic equations on complete manifolds

This page was built for publication: Polynomial bounds for the solutions of parametric transmission problems on smooth, bounded domains

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6667322)