Piecewise linear finite element methods are not localized

DOI10.1090/S0025-5718-03-01584-9zbMath1068.65126OpenAlexW2062383984MaRDI QIDQ4813580

Alan Demlow

Publication date: 13 August 2004

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0025-5718-03-01584-9

zbMATH Keywords

linear finite elementssecond order elliptic problemspointwise errorlocalization of the error

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Error bounds for boundary value problems involving PDEs (65N15) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30)

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Pointwise error estimates for a stabilized Galerkin method: Non-selfadjoint problems ⋮ Local and pointwise error estimates of the local discontinuous Galerkin method applied to the Stokes problem ⋮ Sharply local pointwise a posteriori error estimates for parabolic problems ⋮ Sharply localized pointwise and $W_\infty^{-1}$ estimates for finite element methods for quasilinear problems ⋮ Asymptotically exact a posteriori estimators for the pointwise gradient error on each element in irregular meshes. Part II: The piecewise linear case

Cites Work

• Asymptotic error expansion and Richardson extrapolation for linear finite elements
• Asymptotically exact a posteriori estimators for the pointwise gradient error on each element in irregular meshes. Part 1: A smooth problem and globally quasi-uniform meshes
• Pointwise error estimates and asymptotic error expansion inequalities for the finite element method on irregular grids: Part I. Global estimates
• Asymptotically exact a posteriori estimators for the pointwise gradient error on each element in irregular meshes. Part II: The piecewise linear case
• An Optimal $L_\infty $ Error Estimate for Galerkin Approximations to Solutions of Two-Point Boundary Value Problems