Fractional Space-Time Variational Formulations of (Navier--) Stokes Equations

DOI10.1137/15M1051725zbMath1375.35329OpenAlexW2725298667MaRDI QIDQ5274920

Christoph Schwab, Rob P. Stevenson

Publication date: 7 July 2017

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/15m1051725

zbMATH Keywords

waveletsNavier-Stokes equationsinterpolation spacesparabolic PDEsspace-time variational formulations

Mathematics Subject Classification ID

Variational methods applied to PDEs (35A15) Stokes and related (Oseen, etc.) flows (76D07) Navier-Stokes equations (35Q30) Numerical methods for wavelets (65T60) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Euler equations (35Q31)

Related Items (13)

Space-time \(hp\)-approximation of parabolic equations ⋮ A Well-Posed First Order System Least Squares Formulation of the Instationary Stokes Equations ⋮ A reduced basis method for fractional diffusion operators. I ⋮ Exponential convergence of hp-time-stepping in space-time discretizations of parabolic PDES ⋮ A space-time variational method for optimal control problems: well-posedness, stability and numerical solution ⋮ A variational approach to Navier–Stokes ⋮ Coercive space-time finite element methods for initial boundary value problems ⋮ An optimal adaptive tensor product wavelet solver of a space-time FOSLS formulation of parabolic evolution problems ⋮ A note on the efficient evaluation of a modified Hilbert transformation ⋮ An exact realization of a modified Hilbert transformation for space-time methods for parabolic evolution equations ⋮ Efficient Direct Space-Time Finite Element Solvers for Parabolic Initial-Boundary Value Problems in Anisotropic Sobolev Spaces ⋮ Further results on a space-time FOSLS formulation of parabolic PDEs ⋮ Mild solutions to time fractional stochastic 2D-Stokes equations with bounded and unbounded delay

Cites Work

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• Adaptive wavelet methods for linear and nonlinear least-squares problems
• Space-time discretization of the heat equation
• Space-time finite element methods for parabolic problems
• Weak solution for an abstract Cauchy problem of parabolic type
• Optimal error estimates for linear parabolic problems under minimal regularity assumptions
• Compact sets in the space \(L^ p(0,T;B)\)
• A regularity result for the Stokes problem in a convex polygon
• A uniformly stable Fortin operator for the Taylor-Hood element
• Optimal results for the nonhomogeneous initial-boundary value problem for the two-dimensional Navier-Stokes equations
• Space-time isogeometric analysis of parabolic evolution problems
• The regularity of the Stokes operator and the Fujita-Kato approach to the Navier-Stokes initial value problem in Lipschitz domains
• Stability of Petrov-Galerkin discretizations: application to the space-time weak formulation for parabolic evolution problems
• Résolution d'EDP par un schéma en temps «pararéel »
• Multilevel preconditioning and low-rank tensor iteration for space-time simultaneous discretizations of parabolic PDEs
• Sparse Tensor Product Wavelet Approximation of Singular Functions
• Space-time adaptive wavelet methods for parabolic evolution problems
• Adaptive Wavelet Schemes for Parabolic Problems: Sparse Matrices and Numerical Results
• Initial-Boundary Value Problems for Parabolic Equations
• The h-p version of the finite element method for parabolic equations. Part I. The p-version in time
• Adaptive wavelet methods for elliptic operator equations: Convergence rates
• Stationary Stokes and Navier–Stokes Systems on Two- or Three-Dimensional Domains with Corners. Part I. Linearized Equations
• Lp-Theory for Incompressible Newtonian Flows
• Element-by-Element Construction of Wavelets Satisfying Stability and Moment Conditions
• The h‐p version of the finite element method for parabolic equations. II. The h‐p version in time
• An improved error bound for reduced basis approximation of linear parabolic problems
• Space-time variational saddle point formulations of Stokes and Navier–Stokes equations
• Solvability and maximal regularity of parabolic evolution equations with coefficients continuous in time

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