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In this paper, we present a family of new mixed finite element methods for linear elasticity for both spatial dimensions $n=2,3$, which yields a conforming and strongly symmetric approximation for stress. Applying…

Numerical Analysis · Mathematics 2017-04-26 Shihua Gong , Shuonan Wu , Jinchao Xu

The breakdown of finite element (FEM) computations for the flow of an Oldroyd-B fluid around a cylinder confined between parallel plates, at Weissenberg numbers Wi = O(1), is shown to arise due to a coil-stretch transition experienced by…

Soft Condensed Matter · Physics 2020-07-03 Mohit Bajaj , Matteo Pasquali , J. Ravi Prakash

In this paper, we prove the global existence of analytical solutions to the compressible Oldroyd-B model without retardation near a non-vacuum equilibrium in ${\mathbb R}^n$ $(n=2,3)$. Zero retardation results in zero dissipation in the…

Analysis of PDEs · Mathematics 2023-06-01 Xinghong Pan

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…

Numerical Analysis · Mathematics 2019-02-22 Endre Süli , Tabea Tscherpel

We propose and analyze a mixed formulation for the Brinkman-Forchheimer equations for unsteady flows. Our approach is based on the introduction of a pseudostress tensor related to the velocity gradient, leading to a mixed formulation where…

Numerical Analysis · Mathematics 2020-09-01 Sergio Caucao , Ivan Yotov

We analyze a system of PDEs governing the interaction between two compressible mutually noninteracting fluids and a shell of Koiter type encompassing a time dependent 3D domain filled by the fluids. The dynamics of the fluids is modelled by…

Analysis of PDEs · Mathematics 2023-02-13 Martin Kalousek , Sourav Mitra , Šárka Nečasová

One way of improving the behavior of finite element schemes for classical, time-dependent Maxwell's equations, is to render them from their hyperbolic character to elliptic form. This paper is devoted to the study of the stabilized linear…

Numerical Analysis · Mathematics 2024-09-23 M. Asadzadeh , L. Beilina

In recent years, non-Newtonian fluids have received much attention due to their numerous applications, such as plastic manufacture and extrusion of polymer fluids. They are more complex than Newtonian fluids because the relationship between…

Numerical Analysis · Mathematics 2019-01-23 Libo Feng , Fawang Liu , Ian Turner , Liancun Zheng

We consider a dynamical elasto-plasticity system with Kelvin--Voigt viscosity and linear kinematic hardening of Melan--Prager type. The model is formulated in a variational framework in which a constraint set for the stress evolves in time…

Analysis of PDEs · Mathematics 2026-03-02 Yoshiho Akagawa , Kazunori Matsui

We consider the Cauchy problem ($\mathbb{R}^d, d=2,3$) and the initial boundary values problem ($\mathbb{T}^d, d=2,3$)associated to the compressible Oldroyd-B model which is first derived by Barrett, Lu and S\"{u}li [Existence of large-data…

Analysis of PDEs · Mathematics 2024-08-29 Yajuan Zhao , Yongsheng Li , Tao Liang , Xiaoping Zhai

We consider two models of a compressible inviscid isentropic two-fluid flow. The first one describes the liquid-gas two-phase flow. The second one can describe the mixture of two fluids of different densities or the mixture of fluid and…

Analysis of PDEs · Mathematics 2019-05-01 Lizhi Ruan , Yuri Trakhinin

The aim of this contribution is to address the convergence study of a time and space approximation scheme for an Allen-Cahn problem with constraint and perturbed by a multiplicative noise of It\^o type. The problem is set in a bounded…

Numerical Analysis · Mathematics 2025-09-03 Caroline Bauzet , Cédric Sultan , Guy Vallet , Aleksandra Zimmermann

This paper concerns the global-in-time evolution of a generic compressible two-fluid model in $\mathbb{R}^d$ ($d\geq3$) with the common pressure law. Due to the non-dissipative properties for densities and two different particle paths…

Analysis of PDEs · Mathematics 2025-02-11 Ling-Yun Shou , Jiayan Wu , Lei Yao , Yinghui Zhang

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

Analysis of PDEs · Mathematics 2011-12-21 John W. Barrett , Endre Süli

We consider a model of a viscoelastic compressible flow in $R^{3}$ which is additionally shear thickening (the stress tensor corresponds to the power law model, however, the divergence of the velocity is due to the model bounded). We prove…

Analysis of PDEs · Mathematics 2025-10-14 Yong Lu , Milan Pokorny

In this paper, we investigate a generic compressible two-fluid model with common pressure ($P^+=P^-$) in $\mathbb{R}^3$. Under some smallness assumptions, Evje-Wang-Wen [Arch Rational Mech Anal 221:1285--1316, 2016] obtained the global…

Analysis of PDEs · Mathematics 2022-04-25 Guochun Wu , Lei Yao , Yinghui Zhang

We show the existence of global-in-time weak solutions to a general class of coupled Hookean-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

In this paper we study the numerical error arising in the space-time approximation of unsteady generalized Newtonian fluids which possess a stress-tensor with $(p,\delta)$-structure. A semi-implicit time-discretization scheme coupled with…

Numerical Analysis · Mathematics 2013-07-30 Luigi C. Berselli , Lars Diening , Michael Ruzicka

This paper develops and analyzes a class of semi-discrete and fully discrete weak Galerkin finite element methods for unsteady incompressible convective Brinkman-Forchheimer equations. For the spatial discretization, the methods adopt the…

Numerical Analysis · Mathematics 2024-10-30 Xiaojuan Wang , Jihong Xiao , Xiaoping Xie , Shiquan Zhang

In this paper, we propose a linear and monolithic finite element method for the approximation of an incompressible viscous fluid interacting with an elastic and deforming plate. We use the arbitrary Lagrangian-Eulerian (ALE) approach that…

Numerical Analysis · Mathematics 2023-01-13 Sebastian Schwarzacher , Bangwei She , Karel Tuma