L ∞ -Bounds for the L 2-Projection onto Linear Spline Spaces

DOI10.1007/978-1-4614-4565-4_24zbMath1273.65180OpenAlexW943322457MaRDI QIDQ2840659

Peter Oswald

Publication date: 23 July 2013

Published in: Springer Proceedings in Mathematics & Statistics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-1-4614-4565-4_24

Mathematics Subject Classification ID

Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Spline approximation (41A15)

Related Items (4)

Balanced-norm error estimates for sparse grid finite element methods applied to singularly perturbed reaction-diffusion problems ⋮ An energy stable discontinuous Galerkin time-domain finite element method in optics and photonics ⋮ Error estimations in the balanced norm of finite element method on Bakhvalov-Shishkin triangular mesh for reaction-diffusion problems ⋮ Robust error estimation in energy and balanced norms for singularly perturbed fourth order problems

Cites Work

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• The stability in L\(^q\) of the L\(^2\)-projection into finite element function spaces
• \(hp\)-finite element methods for singular perturbations
• Convergence and stability in balanced norms of finite element methods on Shishkin meshes for reaction‐diffusion problems
• Robust Numerical Methods for Singularly Perturbed Differential Equations
• On the Angle Condition in the Finite Element Method
• A counterexample concerning the $L_2$-projector onto linear spline spaces
• On Finite Element Matrices
• Properties of the orthonormal Franklin system
• The \(L_\infty\)-norm of the \(L_2\)-spline projector is bounded independently of the knot sequence: A proof of de Boor's conjecture

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