Optimality of a Standard Adaptive Finite Element Method for the Stokes Problem
DOI10.1137/17M1153170zbMath1422.65383arXiv1710.08289OpenAlexW2945213929MaRDI QIDQ5232281
Publication date: 2 September 2019
Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1710.08289
PDEs in connection with fluid mechanics (35Q35) Navier-Stokes equations for incompressible viscous fluids (76D05) 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) Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs (65N50) Direct numerical methods for linear systems and matrix inversion (65F05)
Related Items
Cites Work
- Unnamed Item
- Axioms of adaptivity
- On 2D newest vertex bisection: optimality of mesh-closure and \(H ^{1}\)-stability of \(L _{2}\)-projection
- On the equivalence of fractional-order Sobolev semi-norms
- Convergence and quasi-optimality of an adaptive finite element method for controlling \(L_{2}\) errors
- Propriétés des matrices ``bien localisées près de leur diagonale et quelques applications. (Properties of matrices ``well localized near the diagonal and some applications)
- Localization of matrix factorizations
- Convergence of a standard adaptive nonconforming finite element method with optimal complexity
- Stability of multiscale transformations
- LU-factorization of order bounded operators on Banach sequence spaces
- Adaptive finite element methods with convergence rates
- Convergence and complexity of arbitrary order adaptive mixed element methods for the Poisson equation
- Optimal adaptive nonconforming FEM for the Stokes problem
- Quasi-optimal convergence rates for adaptive boundary element methods with data approximation. I: Weakly-singular integral equation
- Quasi-optimal convergence rates for adaptive boundary element methods with data approximation. II: Hyper-singular integral equation
- Energy norm based error estimators for adaptive BEM for hypersingular integral equations
- Adaptive boundary element methods with convergence rates
- Convergence and optimality of the adaptive nonconforming linear element method for the Stokes problem
- Decay rates of adaptive finite elements with Dörfler marking
- A natural adaptive nonconforming FEM of quasi-optimal complexity
- Optimality of a standard adaptive finite element method
- Quasi-optimal Convergence Rate for an Adaptive Boundary Element Method
- The Adaptive Nonconforming FEM for the Pure Displacement Problem in Linear Elasticity is Optimal and Robust
- Convergence and optimality of adaptive mixed finite element methods
- A Convergent Nonconforming Adaptive Finite Element Method with Quasi-Optimal Complexity
- A convergence proof for adaptive finite elements without lower bound
- Quasi-Optimality of Adaptive Nonconforming Finite Element Methods for the Stokes Equations
- Quasioptimal cardinality of AFEM driven by nonresidual estimators
- Error estimates for a mixed finite element approximation of the Stokes equations
- Finite Element Interpolation of Nonsmooth Functions Satisfying Boundary Conditions
- 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
- Mixed and Hybrid Finite Element Methods
- STABILITY OF HIGHER ORDER TRIANGULAR HOOD-TAYLOR METHODS FOR THE STATIONARY STOKES EQUATIONS
- Instance optimal Crouzeix–Raviart adaptive finite element methods for the Poisson and Stokes problems:
- An Adaptive Uzawa FEM for the Stokes Problem: Convergence without the Inf-Sup Condition
- Efficiency and Optimality of Some Weighted-Residual Error Estimator for Adaptive 2D Boundary Element Methods
- The completion of locally refined simplicial partitions created by bisection
- Adaptive FEM with Optimal Convergence Rates for a Certain Class of Nonsymmetric and Possibly Nonlinear Problems
- Instance optimality of the adaptive maximum strategy