Optimal adaptive nonconforming FEM for the Stokes problem

DOI10.1007/s00211-012-0490-8zbMath1316.76046OpenAlexW2140677965MaRDI QIDQ1938056

Daniel Peterseim, Hella Rabus, Carsten Carstensen

Publication date: 1 February 2013

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

Full work available at URL: https://nbn-resolving.org/urn:nbn:de:bvb:384-opus4-434484

zbMATH Keywords

a posteriori error estimatoroptimal convergence ratecontraction propertydiscrete Helmholtz decompositionquasi-optimal complexity

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) Finite element methods applied to problems in fluid mechanics (76M10)

Related Items (21)

Convergence of adaptive nonconforming finite element method for Stokes optimal control problems ⋮ Axioms of adaptivity ⋮ A discrete Helmholtz decomposition with morley finite element functions and the optimality of adaptive finite element schemes ⋮ A low-order discontinuous Petrov-Galerkin method for the Stokes equations ⋮ State space Newton's method for topology optimization ⋮ \(h\)-adaptive least-squares finite element methods for the 2D Stokes equations of any order with optimal convergence rates ⋮ Inf-sup stability implies quasi-orthogonality ⋮ A parameter-free mixed formulation for the Stokes equations and linear elasticity with strongly symmetric stress ⋮ A Unified Analysis of Quasi-Optimal Convergence for Adaptive Mixed Finite Element Methods ⋮ A mixed finite element method for the Stokes equations based on a weakly over-penalized symmetric interior penalty approach ⋮ A contraction property of an adaptive divergence-conforming discontinuous Galerkin method for the Stokes problem ⋮ On the threshold condition for Dörfler marking ⋮ An adaptive least-squares FEM for the Stokes equations with optimal convergence rates ⋮ A robust prolongation operator for non-nested finite element methods ⋮ Adaptive nonconforming Crouzeix-Raviart FEM for eigenvalue problems ⋮ Contraction property of adaptive hybridizable discontinuous Galerkin methods ⋮ Recurrent neural networks as optimal mesh refinement strategies ⋮ Adaptive Uzawa algorithm for the Stokes equation ⋮ Optimality of a Standard Adaptive Finite Element Method for the Stokes Problem ⋮ Forty Years of the Crouzeix‐Raviart element ⋮ Lightning Stokes Solver

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