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We prove the existence of global-in-time weak solutions to a general class of models that arise from the kinetic theory of dilute solutions of nonhomogeneous polymeric liquids, where the polymer molecules are idealized as bead-spring chains…

Analysis of PDEs · Mathematics 2015-07-21 John W. Barrett , Endre Süli

We develop a finite element discretization for the weakly symmetric equations of linear elasticity on tetrahedral meshes. The finite element combines, for $r \geq 0$, discontinuous polynomials of $r$ for the displacement,…

Numerical Analysis · Mathematics 2018-02-09 Tobin Isaac

The motion of incompressible fractional Oldroyd-B fluids between two parallel walls perpendicular to a plate that applies time-dependent shear stresses to the fluid is studied by means of integral transforms. In the special cases of…

Fluid Dynamics · Physics 2014-08-21 Azhar Ali Zafar , Constantin Fetecau , Itrat Abbas Mirza

When discretizing symmetric stress tensors in variational problems arising in continuum mechanics, one has to choose how to enforce the symmetry of the stress tensor: (i) strongly by requiring the discrete tensors to be pointwise symmetric…

Numerical Analysis · Mathematics 2026-05-21 Pablo Brubeck , Charles Parker , Umberto Zerbinati

This paper establishes a sharp characterization of temporal decay rates for the incompressible Oldroyd-B model in a critical $L^p$ framework, covering the physically relevant and mathematically delicate case where both the fluid viscosity…

Analysis of PDEs · Mathematics 2026-05-14 Zhi Chen , Mingwen Fei , Lvqiao Liu , Jiahong Wu

We show the existence of global-in-time weak solutions to a general class of coupled FENE-type bead-spring chain models that arise from the kinetic theory of dilute solutions of polymeric liquids with noninteracting polymer chains. The…

Analysis of PDEs · Mathematics 2012-09-25 John W. Barrett , Endre Süli

This paper is devoted to the design and analysis of a numerical algorithm for approximating solutions of a degenerate cross-diffusion system, which models particular instances of taxis-type migration processes under local sensing…

Numerical Analysis · Mathematics 2025-10-09 Juan Vicente Gutiérrez-Santacreu

We consider a linearised model of incompressible inviscid flow. Using a regularisation based on the Hodge Laplacian we prove existence and uniqueness of weak solutions for smooth domains. The model problem is then discretised using…

Numerical Analysis · Mathematics 2019-12-09 Gabriel Barrenechea , Erik Burman , Johnny Guzmàn

The positive definite symmetric polymer conformation tensor possesses a unique symmetric square root that satisfies a closed evolution equation in the Oldroyd-B and FENE-P models of viscoelastic fluid flow. When expressed in terms of the…

Numerical Analysis · Mathematics 2010-06-18 Nusret Balci , Becca Thomases , Michael Renardy , Charles R. Doering

Pressure-robust discretizations for incompressible flows have been in the focus of research for the past years. Many publications construct exactly divergence-free methods or use a reconstruction approach [13] for existing methods like the…

Numerical Analysis · Mathematics 2024-01-22 Volker Kempf

In this paper, we propose a discretization for the (nonlinearized) compressible Stokes problem with a linear equation of state $\rho=p$, based on Crouzeix-Raviart elements. The approximation of the momentum balance is obtained by usual…

Numerical Analysis · Mathematics 2008-09-18 Thierry Gallouët , Raphaele Herbin , Jean-Claude Latché

We propose a discrete functional analysis result suitable for proving compactness in the framework of fully discrete approximations of strongly degenerate parabolic problems. It is based on the original exploitation of a result related to…

Numerical Analysis · Mathematics 2015-04-16 Boris Andreianov , Clément Cancès , Ayman Moussa

We study a finite element approximation of a coupled fluid-structure interaction consisting of a three-dimensional incompressible viscous fluid governed by the unsteady Stokes equations and a two-dimensional elastic plate. To avoid the use…

Numerical Analysis · Mathematics 2026-02-10 Lander Besabe , Hyesuk Lee

We prove the existence of weak solutions and a unique strong solution to the Oldroyd-B dumbbell model describing the evolution of a two-dimensional dilute polymer fluid interacting with a one-dimensional viscoelastic shell. The polymer…

Analysis of PDEs · Mathematics 2025-06-13 Prince Romeo Mensah

We consider the Dirichlet problem for a compressible two-fluid model in three dimensions, and obtain the global existence of weak solution with large initial data and independent adiabatic constants \Gamma,\gamma>=9/5. The pressure…

Analysis of PDEs · Mathematics 2021-07-27 Huanyao Wen

We present a novel and comparative analysis of finite element discretizations for a nonlinear Rosenau-Burgers model including a biharmonic term. We analyze both continuous and mixed finite element approaches, providing stability, existence,…

Numerical Analysis · Mathematics 2024-02-15 Ankur , Ram Jiwari , Akil Narayan

We study the generalized Oldroyd model with viscosity depending on the shear stress behaving like $\mu(\mathbf{D}) \sim |\mathbf{D}|^{p-2}$ ($p>\frac 65$) regularized by a nonlinear stress diffusion. Using the Lipschitz truncation method we…

Analysis of PDEs · Mathematics 2014-07-14 Ondřej Kreml , Milan Pokorný , Pavel Šalom

In this paper, a backward Euler method combined with finite element discretization in spatial direction is discussed for the equations of motion arising in the $2D$ Oldroyd model of viscoelastic fluids of order one with the forcing term…

Numerical Analysis · Mathematics 2026-04-16 Bikram Bir , Deepjyoti Goswami , Amiya K. Pani

We consider a 1D-2V Vlasov-Fokker-Planck multi-species ionic description coupled to fluid electrons. We address temporal stiffness with implicit time stepping, suitably preconditioned. To address temperature disparity in time and space, we…

Plasma Physics · Physics 2018-05-09 William T. Taitano , Luis Chacon , Andrei N. Simakov

We consider the system of partial differential equations governing two-dimensional flows of a robust class of viscoelastic rate-type fluids with stress diffusion, involving a general objective derivative. The studied system generalizes the…

Analysis of PDEs · Mathematics 2022-06-08 Miroslav Bulíček , Josef Málek , Casey Rodriguez