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Related papers: A Stabilized Finite Element Method for Morpho-Visc…

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We carry out the homogenization of a fluid-structure interaction problem consisting in the periodic inclusions of a viscous fluid in an elastic body. We get a macrostructure model where the body behaves as a viscoelastic material with a…

Analysis of PDEs · Mathematics 2024-05-20 Juan Casado-Díaz

We consider finite element discretizations of the Biot's consolidation model in poroelasticity with MINI and stabilized P1-P1 elements. We analyze the convergence of the fully discrete model based on spatial discretization with these types…

Numerical Analysis · Mathematics 2023-07-19 Carmen Rodrigo , Francisco Gaspar , Xiaozhe Hu , Ludmil Zikatanov

We present a stabilised finite element method for modelling proton transport in tissue, incorporating both inelastic energy loss and elastic angular scattering. A key innovation is a positivity-preserving formulation that guarantees…

Numerical Analysis · Mathematics 2025-06-03 Ben S. Ashby , Abdalaziz Hamdan , Tristan Pryer

We analyse the Virtual Element Methods (VEM) on a simple elliptic model problem, allowing for more general meshes than the one typically considered in the VEM literature. For instance, meshes with arbitrarily small edges (with respect to…

Numerical Analysis · Mathematics 2016-07-21 Lourenco Beirao da Veiga , Carlo Lovadina , Alessandro Russo

As two-dimensional fluid shells, lipid bilayer membranes resist bending and stretching but are unable to sustain shear stresses. This property gives membranes the ability to adopt dramatic shape changes. In this paper, a finite element…

Biological Physics · Physics 2009-11-13 Lin Ma , William S. Klug

Modeling the spontaneous evolution of morphology in natural systems and its preservation by proportionate growth remains a major scientific challenge. Yet, it is conceivable that if the basic mechanisms of growth and the coupled kinetic…

Soft Condensed Matter · Physics 2020-12-30 Virginia von Streng , Rami Abi-Akl , Bianca Giovanardi , Tal Cohen

Finite element plate and shell formulations are ubiquitous in structural analysis for modeling all kinds of slender structures, both for static and dynamic analyses. The latter are particularly challenging as the high order nature of the…

Numerical Analysis · Mathematics 2025-09-03 Giuliano Guarino , Yannis Voet , Pablo Antolin , Annalisa Buffa

This paper concerns with finite element approximations of a quasi-static poroelasticity model in displacement-pressure formulation which describes the dynamics of poro-elastic materials under an applied mechanical force on the boundary. To…

Numerical Analysis · Mathematics 2014-12-01 Xiaobing Feng , Zhihao Ge , Yukun Li

We address a three-dimensional model capable of describing coupled damage and plastic effects in solids at finite strains. Formulated within the variational setting of {\it generalized standard materials}, the constitutive model results…

Analysis of PDEs · Mathematics 2020-12-30 David Melching , Michael Neunteufel , Joachim Schöberl , Ulisse Stefanelli

Convection-diffusion equations arise in a variety of applications such as particle transport, electromagnetics, and magnetohydrodynamics. Simulation of the convection-dominated regime for these problems, even with high-fidelity techniques,…

Numerical Analysis · Mathematics 2023-05-24 James H. Adler , Casey Cavanaugh , Xiaozhe Hu , Andy Huang , Nathaniel Trask

This paper is concerned with fully discrete finite element methods for approximating variational solutions of nonlinear stochastic elastic wave equations with multiplicative noise. A detailed analysis of the properties of the weak solution…

Numerical Analysis · Mathematics 2022-10-04 Xiaobing Feng , Yukun Li , Yujian Lin

We investigate the evolution of a two-phase viscoelastic material at finite strains. The phase evolution is assumed to be irreversible: One phase accretes in time in its normal direction, at the expense of the other. Mechanical response…

Analysis of PDEs · Mathematics 2025-01-10 Andrea Chiesa , Ulisse Stefanelli

With the development of multi-layer elastic systems in the field of engineering mechanics, the corresponding variational inequality theory and algorithm design have received more attention and research. In this study, a class of equivalent…

Numerical Analysis · Mathematics 2024-09-11 Zhizhuo Zhang , Mikaël Barboteu , Xiaobing Nie , Serge Dumont , Mahmoud Abdel-Aty , Jinde Cao

The modeling of coupled fluid transport and deformation in a porous medium is essential to predict the various geomechanical process such as CO2 sequestration, hydraulic fracturing, and so on. Current applications of interest, for instance,…

Analysis of PDEs · Mathematics 2022-01-03 Mina Karimi , Mehrdad Massoudi , Noel Walkington , Matteo Pozzi , Kaushik Dayal

We investigate and clarify the mathematical properties of linear poro-elastic systems in the presence of classical (linear, Kelvin-Voigt) visco-elasticity. In particular, we quantify the time-regularizing and dissipative effects of…

Analysis of PDEs · Mathematics 2023-02-07 Lorena Bociu , Boris Muha , Justin T. Webster

In this work, we consider a hybrid mixed finite element method for Biot's model. The hybrid P1-RT0-P0 discretization of the displacement-pressure-Darcy's velocity system of Biot's model presented in \cite{C. Niu} is not uniformly stable…

Numerical Analysis · Mathematics 2020-04-28 Chunyan Niu , Hongxing Rui , Xiaozhe Hu

We consider a stabilized finite element method based on a spacetime formulation, where the equations are solved on a global (unstructured) spacetime mesh. A unique continuation problem for the wave equation is considered, where data is…

Numerical Analysis · Mathematics 2023-05-10 Erik Burman , Ali Feizmohammadi , Arnaud Munch , Lauri Oksanen

The computational modeling of many engineering problems using the Finite Element method involves the modeling of two or more bodies that meet through an interface. The interface can be physical, as in multi-physics and contact problems, or…

Numerical Analysis · Computer Science 2009-09-30 G. Haikal

This work focuses on the numerical solution of the dynamics of a poroelastic material in the frequency domain. We provide a detailed stability analysis based on the application of the Fredholm alternative in the continuous case, considering…

Numerical Analysis · Mathematics 2024-09-17 Cristian Cárcamo , Alfonso Caiazzo , Felipe Galarce , Joaquín Mura

Wave propagation problems have many applications in physics and engineering, and the stochastic effects are important in accurately modeling them due to the uncertainty of the media. This paper considers and analyzes a fully discrete finite…

Numerical Analysis · Mathematics 2021-06-30 Yukun Li , Shuonan Wu , Yulong Xing