A note on interpolation, best approximation, and the saturation property

DOI10.1007/s00211-014-0687-0zbMath1332.65155OpenAlexW2031279569MaRDI QIDQ495533

Harry Yserentant, Randolph E. Bank

Publication date: 14 September 2015

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

Full work available at URL: https://doi.org/10.1007/s00211-014-0687-0

zbMATH Keywords

interpolationSobolev spacefinite elementerror boundbest approximationsaturationelliptic boundary value problem

Mathematics Subject Classification ID

Error bounds for boundary value problems involving PDEs (65N15) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Numerical interpolation (65D05) Interpolation in approximation theory (41A05) Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs (65N50)

Related Items (6)

Adventures in adaptivity ⋮ Local finite element approximation of Sobolev differential forms ⋮ Numerical Homogenization of Elliptic Multiscale Problems by Subspace Decomposition ⋮ Some remarks on interpolation and best approximation ⋮ On the convergence of adaptive feedback loops ⋮ Equivalence of local-best and global-best approximations in \(\boldsymbol{H}(\mathrm{curl})\)

Cites Work

• Unnamed Item
• Approximating gradients with continuous piecewise polynomial functions
• Superconvergent Derivative Recovery for Lagrange Triangular Elements of Degreepon Unstructured Grids
• Polynomial Approximation of Functions in Sobolev Spaces

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