Stability of the Stokes projection on weighted spaces and applications

DOI10.1090/mcom/3509zbMath1437.35572arXiv1905.00476OpenAlexW2991295768MaRDI QIDQ4960068

Enrique Otárola, Abner J. Salgado, Ricardo G. Durán

Publication date: 8 April 2020

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1905.00476

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Error bounds for boundary value problems involving PDEs (65N15) Stokes and related (Oseen, etc.) flows (76D07) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Navier-Stokes equations (35Q30) PDEs with measure (35R06)

Related Items (max. 100)

On the analysis and approximation of some models of fluids over weighted spaces on convex polyhedra ⋮ Analysis of a diffuse interface method for the Stokes-Darcy coupled problem ⋮ An optimal control problem for the Navier-Stokes equations with point sources ⋮ A Posteriori Error Estimates for the Stationary Navier--Stokes Equations with Dirac Measures ⋮ Error estimates for optimal control problems involving the Stokes system and Dirac measures ⋮ Improved error estimates for optimal control of the Stokes problem with pointwise tracking in three dimensions ⋮ A posteriori error estimates in \(W^{1,p}\times L^p\) spaces for the Stokes system with Dirac measures ⋮ Analysis of fully discrete, quasi non-conforming approximations of evolution equations and applications

Cites Work

• Unnamed Item
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• Powers of distances to lower dimensional sets as Muckenhoupt weights
• Max-norm estimates for Stokes and Navier-Stokes approximations in convex polyhedra
• Piecewise polynomial interpolation in Muckenhoupt weighted Sobolev spaces and applications
• A stable finite element for the Stokes equations
• A posteriori error estimators for the Stokes equations
• Über die punktweise Konvergenz finiter Elemente
• Two-weight Sobolev-Poincaré inequalities and Harnack inequality for a class of degenerate elliptic operators
• Weighted \(L^q\)-theory for the Stokes resolvent in exterior domains
• Nonlinear potential theory and weighted Sobolev spaces
• The Poisson and Stokes problems on weighted spaces in Lipschitz domains and under singular forcing
• Maximum-norm stability of the finite element Stokes projection
• Theory and practice of finite elements.
• Finite element convergence for singular data
• A quasi-local interpolation operator preserving the discrete divergence
• An explicit right inverse of the divergence operator which is continuous in weighted norms
• Pointwise error estimates of finite element approximations to the Stokes problem on convex polyhedra
• Divergence Operator and Related Inequalities
• An Introduction to the Mathematical Theory of the Navier-Stokes Equations
• Solutions of the divergence and Korn inequalities on domains with an external cusp
• On some nonuniform cases of the weighted Sobolev and Poincaré inequalities
• A Unified Theory for Some Non-Newtonian Fluids Under Singular Forcing
• Error estimates for a mixed finite element approximation of the Stokes equations
• Finite Element Interpolation of Nonsmooth Functions Satisfying Boundary Conditions
• Sharp Maximum Norm Error Estimates for Finite Element Approximations of the Stokes Problem in 2 - D
• A decomposition technique for John domains
• Weighted Sobolev spaces and embedding theorems
• Weighted Poincare and Sobolev Inequalities and Estimates for Weighted Peano Maximal Functions
• Finite Element Methods for Navier-Stokes Equations
• Generalized Inf-Sup Conditions for Chebyshev Spectral Approximation of the Stokes Problem
• Some Optimal Error Estimates for Piecewise Linear Finite Element Approximations
• The local regularity of solutions of degenerate elliptic equations
• Weighted Inf-Sup Condition and Pointwise Error Estimates for the Stokes Problem
• On Certain Convolution Inequalities
• Finite element approximation of an incompressible chemically reacting non-Newtonian fluid
• A Weighted Setting for the Numerical Approximation of the Poisson Problem with Singular Sources
• Error estimates on anisotropic ${\mathcal Q}_1$ elements for functions in weighted Sobolev spaces
• The Mathematical Theory of Finite Element Methods
• Pointwise Error Estimates for Finite Element Solutions of the Stokes Problem
• Weighted Norm Inequalities for the Hardy Maximal Function

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