Tensor-sparsity of solutions to high-dimensional elliptic partial differential equations by Dahmen, W, DeVore, R, Grasedyck, L, Süli, E

“…A recurring theme in attempts to break the curse of dimensionality in the numerical approximation of solutions to high-dimensional partial differential equations (PDEs) is to employ some form of sparse tensor approximation. Unfortunately, there are only a few results that quantify the possible advantages of such an approach. …”

Finite element approximation for the unsteady flow of implicitly constituted incompressible fluids by Tscherpel, T

“…</p> <p>The constitutive law between shear stress tensor and shear rate tensor is encoded by a (t,x)-dependent maximal monotone graph with q-growth, for q &gt; 1. …”

Existence of global weak solutions to the kinetic Hookean dumbbell model for incompressible dilute polymeric fluids by Barrett, J, Süli, E

“…This model involves the unsteady incompressible Navier-Stokes equations in a bounded domain in two or three space dimensions for the velocity and the pressure of the fluid, with an elastic extra-stress tensor appearing on the right-hand side in the momentum equation. …”

Existence of global weak solutions to compressible isentropic finitely extensible bead-spring chain models for dilute polymers by Barrett, JW, Süli, E

“…The right-hand side of the Navier–Stokes momentum equation includes an elastic extra-stress tensor, which is the sum of the classical Kramers expression and a quadratic interaction term. …”

Existence and equilibration of global weak solutions to finitely extensible nonlinear bead-spring chain models for dilute polymers by Barrett, J, Süli, E

“…The class of models involves the unsteady incompressible Navier-Stokes equations in a bounded domain in two or three space dimensions for the velocity and the pressure of the fluid, with an elastic extra-stress tensor appearing on the right-hand side in the momentum equation. …”

Existence of global weak solutions to finitely extensible nonlinear bead-spring chain models for dilute polymers with variable density and viscosity by Barrett, J, Süli, E

“…The class of models under consideration involves the unsteady incompressible Navier-Stokes equations with variable density and density-dependent dynamic viscosity in a bounded domain in two and three space dimensions, for the density, the velocity and the pressure of the fluid, with an elastic extra-stress tensor appearing on the right-hand side in the momentum equation. …”

Finite element approximation of finitely extensible nonlinear elastic dumbbell models for dilute polymers by Barrett, J, Süli, E

“…The class of models involves the unsteady incompressible Navier-Stokes equations in a bounded domain Ω d, d = 2 or 3, for the velocity and the pressure of the fluid, with an elastic extra-stress tensor appearing on the right-hand side in the momentum equation. …”

Existence and equilibration of global weak solutions to Hookean-type bead-spring chain models for dilute polymers by Barrett, J, Süli, E

“…The class of models involves the unsteady incompressible Navier-Stokes equations in a bounded domain in two or three space dimensions for the velocity and the pressure of the fluid, with an elastic extra-stress tensor appearing on the right-hand side in the momentum equation. …”

Fully discrete finite element approximation of unsteady flows of implicitly constituted incompressible fluids by Süli, E, Tscherpel, T

“…Implicit constitutive theory provides a very general framework for fluid flow models, including both Newtonian and generalized Newtonian fluids, where the Cauchy stress tensor and the rate of strain tensor are assumed to be related by an implicit relation associated with a maximal monotone graph. …”

Existence of large-data finite-energy global weak solutions to a compressible Oldroyd-B model by Barrett, J, Lu, Y, Süli, E

“…We develop a priori bounds for the model, including a logarithmic bound, which guarantee the nonnegativity of the elastic extra stress tensor, and we prove the existence of large data global-in-time finite-energy weak solutions in two space dimensions.…”

Thermodynamics of viscoelastic rate-type fluids with stress diffusion by Málek, J, Průša, V, Skřivan, T, Süli, E

“…In particular, we derive variants of compressible/incompressible Maxwell/Oldroyd-B models with a stress diffusion term in the evolution equation for the extra stress tensor. It is shown that the stress diffusion term can be interpreted either as a consequence of a nonlocal energy storage mechanism or as a consequence of a nonlocal entropy production mechanism. …”

Discontinuous Galerkin Finite Element Approximation of Nonlinear Second-Order Elliptic and Hyperbolic Systems. by Ortner, C, Süli, E

“…Optimal-order asymptotic bounds are derived on the discretization error in each case without requiring the global Lipschitz continuity or uniform monotonicity of the stress tensor. Instead, only local smoothness and a Gårding inequality are used in the analysis. © 2007 Society for Industrial and Applied Mathematics.…”

Nonlinear iterative approximation of steady incompressible chemically reacting flows by Gazca-Orozco, PA, Heid, P, Süli, E

“…We prove that the weak solution, whose existence was already established in the literature, is unique, given some strengthened assumptions on the diffusive flux and the stress tensor, for small enough data. We then show that the uniqueness result can be applied to a model describing the synovial fluid. …”

Numerical analysis of unsteady implicitly constituted incompressible fluids: 3-field formulation by Farrell, P, Gazca-Orozco, P, Süli, E

“…In the classical theory of fluid mechanics a linear relationship between the shear stress and the symmetric velocity gradient tensor is often assumed. Even when a nonlinear relationship is assumed, it is typically formulated in terms of an explicit relation. …”

Corotational Hookean models of dilute polymeric fluids: existence of global weak solutions, weak-strong uniqueness, equilibration and macroscopic closure by Dębiec, T, Süli, E

“…The micro-macro interaction is manifested by the presence of a corotational drag term in the Fokker–Planck equation and the divergence of a polymeric extra-stress tensor on the right-hand side of the Navier–Stokes momentum equation. …”

Dissipative weak solutions to compressible Navier-Stokes-Fokker-Planck systems with variable viscosity coefficients by Feireisl, E, Lu, Y, Süli, E

“…The motion of the solvent is governed by the unsteady, compressible, barotropic Navier--Stokes system, where the viscosity coefficients in the Newtonian stress tensor depend on the polymer number density. Our goal is to show that the existence theory developed in the case of constant viscosity coefficients can be extended to the case of polymer-number-density-dependent viscosities, provided that certain technical restrictions are imposed, relating the behavior of the viscosity coefficients and the pressure for large values of the solvent density. …”

Strain-limiting viscoelasticity by Patel, V

“…The main technical difficulty here is that the sequence of approximate stress tensors is, at best, bounded in L^∞(0,T;L^1(Ω)^{d×d}), which has poor compactness properties. …”

Adaptive Galerkin approximation algorithms for Kolmogorov equations in infinite dimensions by Schwab, C, Süli, E

“…Specifically, for the infinite-dimensional Fokker–Planck equation, adaptive space-time Galerkin discretizations, based on a wavelet polynomial chaos Riesz basis obtained by tensorization of biorthogonal piecewise polynomial wavelet bases in time with a spatial Wiener–Hermite polynomial chaos arising from the Wiener–Itô decomposition of L2(H, μ), are introduced. …”