On the Adaptive Selection of the Parameter in Stabilized Finite Element Approximations

DOI10.1137/110837796zbMath1276.65076OpenAlexW2024034341MaRDI QIDQ2845604

Alejandro Allendes, Gabriel R. Barrenechea, Richard Rankin, Mark Ainsworth

Publication date: 2 September 2013

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://strathprints.strath.ac.uk/44170/

zbMATH Keywords

Stokes problemderivative-free optimizationstabilized finite element methodcomputable error boundsstabilization parameter

Mathematics Subject Classification ID

Error bounds for boundary value problems involving PDEs (65N15) Stokes and related (Oseen, etc.) flows (76D07) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Navier-Stokes equations (35Q30) Finite element methods applied to problems in fluid mechanics (76M10)

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A Posteriori Error Estimation for a PDE-Constrained Optimization Problem Involving the Generalized Oseen Equations ⋮ On adaptive grad-div parameter selection ⋮ A posteriori error estimate for discontinuous Galerkin finite element method on polytopal mesh ⋮ A posteriori error estimate for a modified weak Galerkin method solving elliptic problems ⋮ A Posteriori Error Estimates for a Local Discontinuous Galerkin Approximation of Semilinear Second-Order Elliptic Problems on Cartesian Grids ⋮ Adaptive inexact iterative algorithms based on polynomial-degree-robust a posteriori estimates for the Stokes problem ⋮ A posteriori error estimators for stabilized finite element approximations of an optimal control problem ⋮ Two efficient and reliable a posteriori error estimates for the local discontinuous Galerkin method applied to linear elliptic problems on Cartesian grids ⋮ On error indicators for optimizing parameters in stabilized methods

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