English
Related papers

Related papers: Variational and thermodynamically consistent finit…

200 papers

In this report, we propose a divergence-free preserving mixed finite element method (FEM) for the system of nonlinear fourth-order thermally driven active fluid equations. By introducing two auxiliary variables, we lower the complexity of…

Numerical Analysis · Mathematics 2025-09-24 Nan Zheng , Qingguang Guan , Wenlong Pei , Wenju Zhao

We present a finite element discretisation to model the interaction between a poroelastic structure and an elastic medium. The consolidation problem considers fully coupled deformations across an interface, ensuring continuity of…

Numerical Analysis · Mathematics 2023-06-21 S. Badia , M. Hornkjøl , A. Khan , K. -A. Mardal , A. F. Martín , R. Ruiz-Baier

A recent paper [J. A. Evans, D. Kamensky, Y. Bazilevs, "Variational multiscale modeling with discretely divergence-free subscales", Computers & Mathematics with Applications, 80 (2020) 2517-2537] introduced a novel stabilized finite element…

Numerical Analysis · Mathematics 2021-12-21 Sajje Lee Calfy , John A. Evans , David Kamensky

Within this paper, we introduce partially and fully decoupled time stepping schemes for linear thermo-poroelasticity. This means that the mechanics, heat, and flow equations can be solved sequentially. We provide sufficient conditions on…

Numerical Analysis · Mathematics 2026-03-17 R. Altmann , R. Maier , J. Schmeck

In this article we apply a discrete action principle for the Vlasov--Maxwell equations in a structure-preserving particle-field discretization framework. In this framework the finite-dimensional electromagnetic potentials and fields are…

Numerical Analysis · Mathematics 2021-01-27 Martin Campos Pinto , Katharina Kormann , Eric Sonnendrücker

We construct a structure-preserving finite element method and time-stepping scheme for compressible barotropic magnetohydrodynamics (MHD) both in the ideal and resistive cases, and in the presence of viscosity. The method is deduced from…

Numerical Analysis · Mathematics 2021-10-04 Evan S. Gawlik , François Gay-Balmaz

We introduce and analyze a new mixed finite element method with reduced symmetry for the standard linear model in viscoelasticity. Following a previous approach employed for linear elastodynamics, the present problem is formulated as a…

Numerical Analysis · Mathematics 2020-05-05 Gabriel N. Gatica , Antonio Márquez , Salim Meddahi

Symplectic numerical schemes for reversible dynamical systems predict the solution reliably over large times as well, and are a good starting point for extension to schemes for simulating irreversible situations like viscoelastic wave…

Classical Physics · Physics 2025-07-03 Donát M. Takács , Áron Pozsár , Tamás Fülöp

The paper presents a versatile framework for solids which undergo nonisothermal processes with irreversibly changing microstructure at large strains. It outlines rate-type and incremental variational principles for the full thermomechanical…

Numerical Analysis · Mathematics 2022-04-12 Stephan Teichtmeister , Marc-Andre Keip

Semi-discrete and fully discrete mixed finite element methods are considered for Maxwell-model-based problems of wave propagation in linear viscoelastic solid. This mixed finite element framework allows the use of a large class of existing…

Numerical Analysis · Mathematics 2021-06-16 Hao Yuan , Xiaoping Xie

A method for density-based topology optimization of heat exchangers with two fluids is proposed. The goal of the optimization process is to maximize the heat transfer from one fluid to the other, under maximum pressure drop constraints for…

A variational formulation for nonequilibrium thermodynamics was recently proposed in \cite{GBYo2017a,GBYo2017b} for both discrete and continuum systems. This formulation extends the Hamilton principle of classical mechanics to include…

Mathematical Physics · Physics 2019-04-15 François Gay-Balmaz , Hiroaki Yoshimura

In this paper we propose a time discretization of a system of two parabolic equations describing diffusion-driven atom rearrangement in crystalline matter. The equations express the balances of microforces and microenergy; the two phase…

Analysis of PDEs · Mathematics 2019-02-20 Pierluigi Colli , Gianni Gilardi , Pavel Krejčí , Paolo Podio-Guidugli , Jürgen Sprekels

This paper introduces a novel approach to approximate a broad range of reaction-convection-diffusion equations using conforming finite element methods while providing a discrete solution respecting the physical bounds given by the…

Numerical Analysis · Mathematics 2023-11-28 Abdolreza Amiri , Gabriel R. Barrenechea , Tristan Pryer

As model problem we consider the prototype for flow and transport of a concentration in porous media in an interior domain and couple it with a diffusion process in the corresponding unbounded exterior domain. To solve the problem we…

Numerical Analysis · Mathematics 2018-10-22 Christoph Erath , Günther Of , Francisco-Javier Sayas

In this work, we develop a new compatible finite element formulation of the thermal shallow water equations that conserves energy and mathematical entropies given by buoyancy-related quadratic tracer variances. Our approach relies on…

Fluid Dynamics · Physics 2025-03-18 Tamara A. Tambyah , David Lee , Santiago Badia

A proof of convergence is given for semi- and full discretizations of mean curvature flow of closed two-dimensional surfaces. The numerical method proposed and studied here combines evolving finite elements, whose nodes determine the…

Numerical Analysis · Mathematics 2019-06-27 Balázs Kovács , Buyang Li , Christian Lubich

We develop a virtual element method to solve a convective Brinkman-Forchheimer problem coupled with a heat equation. This coupled model may allow for thermal diffusion and viscosity as a function of temperature. Under standard…

Numerical Analysis · Mathematics 2024-09-05 Danilo Amigo , Felipe Lepe , Enrique Otarola , Gonzalo Rivera

We present results of interface-resolved simulations of heat transfer in suspensions of finite-size neutrally-buoyant spherical particles for solid volume fractions up to 35% and bulk Reynolds numbers from 500 to 5600. An Immersed…

Fluid Dynamics · Physics 2020-07-15 Ali Yousefi , Mehdi Niazi Ardekani , Francesco Picano , Luca Brandt

In this paper, we develop a phase-field model for binary incompressible (quasi-incompressible) fluid with thermocapillary effects, which allows for the different properties (densities, viscosities and heat conductivities) of each component…

Fluid Dynamics · Physics 2015-06-18 Zhenlin Guo , Ping Lin