Zsuppán, Sándor
Published in
Zeitschrift für angewandte Mathematik und Physik

We derive Papkovich–Neuber type representations for the solutions of Navier–Lamé equations in linear elastostatics and of the stationary Stokes equations using exterior calculus on the Euclidean space. We generalize the result for two-dimensional Riemannian manifolds.

Deuring, Paul
Published in
Journal of Mathematical Fluid Mechanics

A representation formula without pressure term is derived for regular solutions to the 3D time-dependent Oseen system in exterior Lipschitz domains. This formula is valid even if no boundary conditions are imposed. It is used in order to exhibit how the velocity decays pointwise in space. It turns out that the rate of this decay depends on Lp\docum...

Hishida, Toshiaki
Published in
Partial Differential Equations and Applications

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Grandmont, Céline Vergnet, Fabien
Published in
Journal of Mathematical Fluid Mechanics

We consider a quasi-static fluid–structure interaction problem where the fluid is modeled by the Stokes equations and the structure is an active elastic material. More precisely, the displacement of the structure satisfies the equations of elasticity with an additional active stress, which models the presence of internal biological motors in the st...

Chernov, A. Marcati, C. Mascotto, L.
Published in
Advances in Computational Mathematics

We analyse the p- and hp-versions of the virtual element method (VEM) for the Stokes problem on polygonal domains. The key tool in the analysis is the existence of a bijection between Poisson-like and Stokes-like VE spaces for the velocities. This allows us to re-interpret the standard VEM for Stokes as a VEM, where the test and trial discrete velo...

Hoang, Thi-Thao-Phuong Lee, Hyesuk
Published in
Journal of Scientific Computing

We study a decoupling iterative algorithm based on domain decomposition for the time-dependent nonlinear Stokes–Darcy model, in which different time steps can be used in the flow region and in the porous medium. The coupled system is formulated as a space-time interface problem based on the interface condition for mass conservation. The nonlinear i...

Neustupa, Tomáš
Published in
Acta Applicandae Mathematicae

We deal with a steady Stokes-type problem, associated with a flow of a Newtonian incompressible fluid through a spatially periodic profile cascade. The used mathematical model is based on the reduction to one spatial period, represented by a bounded 2D domain Ω\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfo...

Hadadifard, Fazel Stefanov, Atanas G.
Published in
Journal of Mathematical Fluid Mechanics

We consider the asymptotic behavior of the surface quasi-geostrophic equation, subject to a small external force. Under suitable assumptions on the forcing, we first construct the steady states and we provide a number of useful a posteriori estimates for them. Importantly, to do so, we only impose minimal cancellation conditions on the forcing func...

Fu, Guosheng Lehrenfeld, Christoph Linke, Alexander Streckenbach, Timo
Published in
Journal of Scientific Computing

Robust discretization methods for (nearly-incompressible) linear elasticity are free of volume-locking and gradient-robust. While volume-locking is a well-known problem that can be dealt with in many different discretization approaches, the concept of gradient-robustness for linear elasticity is new: it assures that dominant gradient fields in the ...

Quesada, Carlos Villon, Pierre Salsac, Anne-Virginie

Microcapsules are liquid droplets enclosed by a thin elastic membrane. Being suspended in an external fluid, they undergo large deformations when flowing. Their deformation can be solved numerically, but the resolution of the fluidstructure interactions (FSI) requires extremely long computation times. This