On \(n\)-widths for elliptic problems

DOI10.1006/jmaa.2000.6862zbMath0963.35047OpenAlexW2027335105MaRDI QIDQ1576982

N. Delaunay

Publication date: 28 June 2001

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jmaa.2000.6862

zbMATH Keywords

\(n\)-widthsrough coefficientssingularity perturbed problem

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) PDEs with low regular coefficients and/or low regular data (35R05) Approximation by arbitrary nonlinear expressions; widths and entropy (41A46)

Related Items (17)

Multiscale-spectral GFEM and optimal oversampling ⋮ A brief survey on numerical methods for solving singularly perturbed problems ⋮ Kolmogorov n-width and Lagrangian physics-informed neural networks: a causality-conforming manifold for convection-dominated PDEs ⋮ Exponential convergence of \textit{hp} FEM for spectral fractional diffusion in polygons ⋮ Angles between subspaces and nearly optimal approximation in GFEM ⋮ Layers and corner singularities in singularly perturbed elliptic problems ⋮ Low-Rank Approximation to Heterogeneous Elliptic Problems ⋮ Optimal approximation of elliptic problems by linear and nonlinear mappings. I ⋮ Flux norm approach to finite-dimensional homogenization approximations with non-separated scales and high contrast ⋮ Sparse operator compression of higher-order elliptic operators with rough coefficients ⋮ Optimal approximation of elliptic problems by linear and nonlinear mappings. II ⋮ Reduced multiscale finite element basis methods for elliptic PDEs with parameterized inputs ⋮ On \(n\)-widths of a Sobolev function class in Orlicz spaces ⋮ Model Order Reduction for Problems with Large Convection Effects ⋮ A learning-based projection method for model order reduction of transport problems ⋮ Exponential Convergence for Multiscale Linear Elliptic PDEs via Adaptive Edge Basis Functions ⋮ Optimal local multi-scale basis functions for linear elliptic equations with rough coefficients

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Direct and inverse error estimates for finite elements with mesh refinements
• The partition of unity finite element method: basic theory and applications
• A priori estimates for the solution of convection-diffusion problems and interpolation on Shishkin meshes
• On n-widths in Sobolev spaces and applications to elliptic boundary value problems
• Über die beste Annäherung von Funktionen einer gegebenen Funktionenklasse
• hp FEM for Reaction-Diffusion Equations I: Robust Exponential Convergence
• n-Widths and Singularly Perturbed Boundary Value Problems
• Special Finite Element Methods for a Class of Second Order Elliptic Problems with Rough Coefficients
• Finite-element methods for singularly perturbed high-order elliptic two-point boundary value problems. I: reaction-diffusion-type problems
• On the robust exponential convergence of hp finite element methods for problems with boundary layers
• Optimal Approximability of Solutions of Singularly Perturbed Two-Point Boundary Value Problems

This page was built for publication: On \(n\)-widths for elliptic problems