Convergence analysis for a finite element approximation of a steady model for electrorheological fluids

DOI10.1007/s00211-015-0735-4zbMath1457.65180arXiv1407.2767OpenAlexW931854690MaRDI QIDQ264109

Dominic Breit, Lars Diening, Luigi C. Berselli

Publication date: 5 April 2016

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1407.2767

zbMATH Keywords

finite element approximationelectrorheological fluids

Mathematics Subject Classification ID

Non-Newtonian fluids (76A05) PDEs in connection with fluid mechanics (35Q35) Error bounds for boundary value problems involving PDEs (65N15) Nonlinear elliptic equations (35J60) 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) Finite element methods applied to problems in fluid mechanics (76M10) Electro- and magnetostatics (78A30)

Related Items (11)

Oscillation constants for Euler type differential equations involving the \(p(t)\)-Laplacian ⋮ Quasi-Newton minimization for the \(p(x)\)-Laplacian problem ⋮ The stability of parabolic problems with nonstandard \(p(x,t)\)-growth ⋮ Numerical analysis of nonlinear parabolic problems with variable exponent and L^1 data ⋮ Effective numerical computation of p ( x )–Laplace equations in 2D ⋮ Asymptotic properties for solutions of differential equations with singular \(p(t)\)-Laplacian ⋮ Non-Newtonian fluids with discontinuous-in-time stress tensor ⋮ Unnamed Item ⋮ Power comparison theorems for oscillation problems for second order differential equations with \(p(t)\)-Laplacian ⋮ Singular solutions of nonlinear differential equations with \(p(t)\)-Laplacian ⋮ Finite element approximation of an incompressible chemically reacting non-Newtonian fluid

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Boundary regularity of shear thickening flows
• Finite element approximation of the Navier-Stokes equations
• Lebesgue and Sobolev spaces with variable exponents
• Modeling, mathematical and numerical analysis of electrorheological fluids.
• On the \(C^{1,\gamma}(\overline \varOmega)\cap W^{2,2}(\varOmega) \) regularity for a class of electro-rheological fluids
• Regularity for minimizers of some variational problems in plasticity theory
• Quasi-norm error bounds for the finite element approximation of a non- Newtonian flow
• An example of a space of \(L^{p(x)}\) on which the Hardy-Littlewood maximal operator is not bounded
• On the modeling of electrorheological materials
• Electrorheological fluids: modeling and mathematical theory
• Regularity results for stationary electro-rheological fluids
• \(C^{1,\alpha}\)-regularity for electrorheological fluids in two dimensions
• Estimates for certain differential operators with finite-dimensional kernel
• Interpolation operators in Orlicz--Sobolev spaces
• SOLENOIDAL LIPSCHITZ TRUNCATION FOR PARABOLIC PDEs
• On the Finite Element Approximation ofp-Stokes Systems
• Analysis of Generalized Newtonian Fluids
• Convergence Analysis for Incompressible Generalized Newtonian Fluid Flows with Nonstandard Anisotropic Growth Conditions
• Fractional estimates for non-differentiable elliptic systems with general growth
• Mixed and Hybrid Finite Element Methods
• Sur l'approximation numérique des écoulements quasi-newtoniens dont la viscosité suit la loi puissance ou la loi de Carreau
• A priori and a posteriori error bounds for a nonconforming linear finite element approximation of a non-newtonian flow
• Finite Element Approximation of the p-Laplacian
• On Analysis of Steady Flows of Fluids with Shear-Dependent Viscosity Based on the Lipschitz Truncation Method
• A regularity result for stationary electrorheological fluids in two dimensions
• EXISTENCE AND REGULARITY OF SOLUTIONS AND THE STABILITY OF THE REST STATE FOR FLUIDS WITH SHEAR DEPENDENT VISCOSITY
• Finite Element Approximation of Some Degenerate Monotone Quasilinear Elliptic Systems
• Finite Element Approximation of the $p(\cdot)$-Laplacian
• On strong solutions of the differential equations modeling the steady flow of certain incompressible generalized Newtonian fluids
• On Lipschitz truncations of Sobolev functions (with variable exponent) and their selected applications
• Mathematical modeling of electrorheological materials

This page was built for publication: Convergence analysis for a finite element approximation of a steady model for electrorheological fluids