Adaptive Uzawa algorithm for the Stokes equation

DOI10.1051/m2an/2019039zbMath1434.65248arXiv1812.11798OpenAlexW3105441462MaRDI QIDQ5216097

Gregor Gantner, Dirk Praetorius, Thomas Führer, Giovanni Di Fratta

Publication date: 14 February 2020

Published in: ESAIM: Mathematical Modelling and Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1812.11798

zbMATH Keywords

adaptive finite element methodUzawa algorithmStokes equationoptimal convergence

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) Iterative numerical methods for linear systems (65F10) Finite element methods applied to problems in fluid mechanics (76M10) Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs (65N50) Rate of convergence, degree of approximation (41A25)

Related Items (2)

Convergence and quasi-optimal cost of adaptive algorithms for nonlinear operators including iterative linearization and algebraic solver ⋮ Krylov improvements of the Uzawa method for Stokes type operator matrices

Cites Work

• Unnamed Item
• Unnamed Item
• Axioms of adaptivity
• On 2D newest vertex bisection: optimality of mesh-closure and \(H ^{1}\)-stability of \(L _{2}\)-projection
• A remark on newest vertex bisection in any space dimension
• Adaptive BEM with inexact PCG solver yields almost optimal computational costs
• Fast computation in adaptive tree approximation
• Adaptive finite element methods with convergence rates
• Optimal adaptive nonconforming FEM for the Stokes problem
• Optimal convergence behavior of adaptive FEM driven by simple \((h-h/2)\)-type error estimators
• Adaptive FEM with coarse initial mesh guarantees optimal convergence rates for compactly perturbed elliptic problems
• Convergence and optimality of the adaptive nonconforming linear element method for the Stokes problem
• Convergence rates of adaptive methods, Besov spaces, and multilevel approximation
• Optimality of a standard adaptive finite element method
• A PROOF OF THE INF–SUP CONDITION FOR THE STOKES EQUATIONS ON LIPSCHITZ DOMAINS
• A convergence proof for adaptive finite elements without lower bound
• Quasi-Optimality of Adaptive Nonconforming Finite Element Methods for the Stokes Equations
• A BASIC CONVERGENCE RESULT FOR CONFORMING ADAPTIVE FINITE ELEMENTS
• An Optimal Adaptive Finite Element Method for the Stokes Problem
• Quasi-Optimal Convergence Rate for an Adaptive Finite Element Method
• Convergence rates for adaptive finite elements
• Tree Approximation for hp-Adaptivity
• An Adaptive Uzawa FEM for the Stokes Problem: Convergence without the Inf-Sup Condition
• Adaptive Wavelet Methods for Saddle Point Problems---Optimal Convergence Rates

This page was built for publication: Adaptive Uzawa algorithm for the Stokes equation