\(h\)-adaptive least-squares finite element methods for the 2D Stokes equations of any order with optimal convergence rates

DOI10.1016/j.camwa.2017.02.019zbMath1402.65150OpenAlexW2605593836MaRDI QIDQ1668557

Philipp Bringmann, Carsten Carstensen

Publication date: 29 August 2018

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.camwa.2017.02.019

zbMATH Keywords

Stokes equationsadaptive finite element methodquasi-optimal convergenceleast squares finite element methodhigher-order discretizationseparate marking

Mathematics Subject Classification ID

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) Boundary element methods applied to problems in fluid mechanics (76M15)

Related Items

Adaptive Least-Squares, Discontinuous Petrov-Galerkin, and Hybrid High-Order Methods ⋮ A Discontinuous Petrov–Galerkin Method for Reissner–Mindlin Plates ⋮ How to prove optimal convergence rates for adaptive least-squares finite element methods ⋮ A robust DPG method for large domains ⋮ Computation of the LBB Constant for the Stokes Equation with a Least-Squares Finite Element Method ⋮ Further results on a space-time FOSLS formulation of parabolic PDEs

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Axioms of adaptivity
• An adaptive least-squares FEM for the Stokes equations with optimal convergence rates
• Least-squares finite element methods
• A posteriori error estimators for the Stokes equations
• Elliptic boundary value problems on corner domains. Smoothness and asymptotics of solutions
• Elliptic problems in domains with piecewise smooth boundaries
• Fast computation in adaptive tree approximation
• Adaptive finite element methods with convergence rates
• Optimal adaptive nonconforming FEM for the Stokes problem
• Convergence of natural adaptive least squares finite element methods
• Optimality of a standard adaptive finite element method
• EachH^1/2–stable projection yields convergence and quasi–optimality of adaptive FEM with inhomogeneous Dirichlet data in R^d
• Quasi-optimal Adaptive Pseudostress Approximation of the Stokes Equations
• Convergence and Optimality of Adaptive Least Squares Finite Element Methods
• An optimal adaptive mixed finite element method
• Finite element exterior calculus, homological techniques, and applications
• Finite Element Interpolation of Nonsmooth Functions Satisfying Boundary Conditions
• ERROR ANALYSIS OF MIXED-INTERPOLATED ELEMENTS FOR REISSNER-MINDLIN PLATES
• Preconditioning in H(𝑑𝑖𝑣) and applications
• A comparison of adaptive refinement techniques for elliptic problems
• Axioms of Adaptivity with Separate Marking for Data Resolution
• An Adaptive Least-Squares FEM for Linear Elasticity with Optimal Convergence Rates
• Least-Squares Methods for Incompressible Newtonian Fluid Flow: Linear Stationary Problems
• Mixed Finite Element Methods and Applications
• Finite Elemente
• The completion of locally refined simplicial partitions created by bisection
• The Mathematical Theory of Finite Element Methods
• An a posteriori error estimate for a first-kind integral equation
• On Least-Squares Finite Element Methods for the Poisson Equation and Their Connection to the Dirichlet and Kelvin Principles

This page was built for publication: \(h\)-adaptive least-squares finite element methods for the 2D Stokes equations of any order with optimal convergence rates