Computation of the LBB Constant for the Stokes Equation with a Least-Squares Finite Element Method
DOI10.1137/18M1231183zbMath1437.76024MaRDI QIDQ5210538
Publication date: 21 January 2020
Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)
Stokes problemCosserat spectrumLSFEMLBB constantnoncompact eigenvalue problemellipticity constantupper eigenvalue bound
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) Navier-Stokes equations (35Q30) Finite element methods applied to problems in fluid mechanics (76M10) Numerical methods for eigenvalue problems for boundary value problems involving PDEs (65N25)
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- mfem
- Stokes elements on cubic meshes yielding divergence-free approximations
- Adaptive nonconforming finite element approximation of eigenvalue clusters
- Estimates of the distance to the set of solenoidal vector fields and applications to a posteriori error control
- An adaptive least-squares FEM for the Stokes equations with optimal convergence rates
- Analysis of a velocity-pressure-pseudostress formulation for the stationary Stokes equations
- A priori and a posteriori error analyses of a velocity-pseudostress formulation for a class of quasi-Newtonian Stokes flows
- On the spectrum of the Stokes operator
- Solutions of the divergence operator on John domains
- A posteriori estimates for partial differential equations
- On inequalities of Korn, Friedrichs and Babuska-Aziz
- On inequalities of Friedrichs and Babuška-Aziz in dimension three
- On inequalities of Friedrichs and Babuška-Aziz
- \(h\)-adaptive least-squares finite element methods for the 2D Stokes equations of any order with optimal convergence rates
- A numerical existence proof of nodal lines for the first eigenfunction of the plate equation
- An optimal adaptive FEM for eigenvalue clusters
- On the inequalities of Babuška-Aziz, Friedrichs and Horgan-Payne
- On variational representations of the constant in the inf-sup condition for the Stokes problem
- On the LBB condition in the numerical analysis of the Stokes equations
- Error-bounds for finite element method
- Continuity Properties of the Inf-Sup Constant for the Divergence
- Guaranteed velocity error control for the pseudostress approximation of the Stokes equations
- Finite Element Approximation of Steady Flows of Incompressible Fluids with Implicit Power-Law-Like Rheology
- Quasi-optimal Adaptive Pseudostress Approximation of the Stokes Equations
- Mixed Finite Element Methods for Incompressible Flow: Stationary Navier–Stokes Equations
- A Priori and A Posteriori Pseudostress-velocity Mixed Finite Element Error Analysis for the Stokes Problem
- Estimates of deviations from exact solutions for boundary-value problems with incompressibility condition
- Stability and approximability of the 1–0 element for Stokes equations
- A Multigrid Method for the Pseudostress Formulation of Stokes Problems
- Augmented Mixed Finite Element Methods for the Stationary Stokes Equations
- Pseudostress-velocity formulation for incompressible Navier-Stokes equations
- Mixed finite element methods for incompressible flow: Stationary Stokes equations
- Norm estimates for a maximal right inverse of the divergence operator in spaces of piecewise polynomials
- Eigenvalue Approximation by Mixed and Hybrid Methods
- General Rayleigh Quotient Iteration
- On the LBB constant on stretched domains
- Asymptotic Exactness of the Least-Squares Finite Element Residual
- Least-Squares Methods for Incompressible Newtonian Fluid Flow: Linear Stationary Problems
- Rayleigh–Ritz approximation of the inf-sup constant for the divergence
- Arnold--Winther Mixed Finite Elements for Stokes Eigenvalue Problems
- Mixed Finite Element Methods and Applications
- An elementary proof of the continuity from $L_0^2(\Omega)$ to $H^1_0(\Omega)^n$ of Bogovskii's right inverse of the divergence
- Divergence operator and Poincaré inequalities on arbitrary bounded domains
- The inf‐sup constant for the divergence on corner domains
- A finite element analysis of a pseudostress formulation for the Stokes eigenvalue problem
- Finite Elemente
- The approximation of the Maxwell eigenvalue problem using a least-squares method
- Three Matlab Implementations of the Lowest-order Raviart-Thomas Mfem with a Posteriori Error Control
- Introduction
- A posteriori estimates for the Stokes problem
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