Inf-sup stability implies quasi-orthogonality
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Publication:5097369
DOI10.1090/mcom/3748zbMath1503.65292arXiv2008.12198OpenAlexW3080636957MaRDI QIDQ5097369
Publication date: 23 August 2022
Published in: Mathematics of Computation (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2008.12198
Factorization of matrices (15A23) Stokes and related (Oseen, etc.) flows (76D07) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Numerical computation of matrix norms, conditioning, scaling (65F35) Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs (65N50)
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Cites Work
- Axioms of adaptivity
- Classical FEM-BEM coupling methods: nonlinearities, well-posedness, and adaptivity
- A posteriori error estimates for the Johnson-Nédélec FEM-BEM coupling
- Adaptive mesh refinement -- theory and applications. Proceedings of the Chicago workshop on adaptive mesh refinement methods, Chicago, IL, USA, September 3--5, 2003.
- Poincaré and Sobolev type inequalities for vector-valued functions
- A feedback finite element method with a posteriori error estimation. I: The finite element method and some basic properties of the a posteriori error estimator
- Some observations on Babuška and Brezzi theories
- LU-factorization of order bounded operators on Banach sequence spaces
- Automatic control and adaptive time-stepping
- 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
- Adaptive boundary element methods with convergence rates
- Decay rates of adaptive finite elements with Dörfler marking
- A natural adaptive nonconforming FEM of quasi-optimal complexity
- Efficient implementation of adaptive P1-FEM in Matlab
- Optimality of a standard adaptive finite element method
- Pinching, Trimming, Truncating, and Averaging of Matrices
- Convergence of some adaptive FEM-BEM coupling for elliptic but possibly nonlinear interface problems
- 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
- A-Stable Time Discretizations Preserve Maximal Parabolic Regularity
- Convergence and optimality of adaptive mixed finite element methods
- Space-time adaptive wavelet methods for parabolic evolution problems
- The Validity of Johnson–Nédélec's BEM–FEM Coupling on Polygonal Interfaces
- Quasi-Optimal Convergence Rate of an Adaptive Discontinuous Galerkin Method
- Quasi-Optimality of Adaptive Nonconforming Finite Element Methods for the Stokes Equations
- Quasioptimal cardinality of AFEM driven by nonresidual estimators
- Finite Element Interpolation of Nonsmooth Functions Satisfying Boundary Conditions
- An a Posteriori Error Estimate and Adaptive Timestep Control for a Backward Euler Discretization of a Parabolic Problem
- A BASIC CONVERGENCE RESULT FOR CONFORMING ADAPTIVE FINITE ELEMENTS
- Quasi-Optimal Convergence Rate for an Adaptive Finite Element Method
- Lipschitz Continuity of Functions of Operators in the Schatten Classes
- On the Coupling of Boundary Integral and Finite Element Methods
- Mixed and Hybrid Finite Element Methods
- Three-Dimensional Finite Element Methods for the Stokes Problem
- Data Oscillation and Convergence of Adaptive FEM
- Accuracy and Stability of Numerical Algorithms
- A Convergent Adaptive Algorithm for Poisson’s Equation
- Rate optimality of adaptive finite element methods with respect to overall computational costs
- Optimality of a Standard Adaptive Finite Element Method for the Stokes Problem
- Local inverse estimates for non-local boundary integral operators
- 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
- The main triangle projection in matrix spaces and its applications
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