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We present a numerical model for the dynamics of thin viscous threads based on a discrete, Lagrangian formulation of the smooth equations. The model makes use of a condensed set of coordinates, called the centerline/spin representation: the…
In the mechanics of inviscid conservative fluids, it is classical to generate the equations of dynamics by formulating with adequate variables, that the pressure integral calculated in the time-space domain corresponding to the motion of…
We discuss the stick-slip motion of an elastic block sliding along a rigid substrate. We argue that for a given external shear stress this system shows a discontinuous nonequilibrium transition from a uniform stick state to uniform sliding…
We derive a formulation of the nonhydrostatic equations in spherical geometry with a Lorenz staggered vertical discretization. The combination conserves a discrete energy in exact time integration when coupled with a mimetic horizontal…
Based on relative energy estimates, we study the stability of solutions to the Cahn-Hilliard equation with concentration dependent mobility with respect to perturbations. As a by-product of our analysis, we obtain a weak-strong uniqueness…
An abstract 2nd-order evolution equation or inclusion is discretised in time in such a way that the energy is conserved at least in qualified cases, typically in the cases when the governing energy is component-wise quadratic or…
Numerically simulating deformations in thin elastic sheets is a challenging problem in computational mechanics due to destabilizing compressive stresses that result in wrinkling. Determining the location, structure, and evolution of…
An extension of the two-step staggered time discretization of linear elastodynamics in stress-velocity form to systems involving internal variables subjected to a possibly non-linear dissipative evolution is proposed. The original scheme is…
We propose and analyse an augmented mixed finite element method for the Oseen equations written in terms of velocity, vorticity, and pressure with non-constant viscosity and homogeneous Dirichlet boundary condition for the velocity. The…
We develop an unconditionally energy-stable tensor-product space-time discretization framework for the solution of a linear kinetic transport equation in one space dimension. The kinetic equation is a simplified model of radiative transfer…
We present a model for the dynamics of elastic or poroelastic bodies with monopolar repulsive long-range (electrostatic) interactions at large strains. Our model respects (only) locally the non-self-interpenetration condition but can cope…
Using the T-coercivity theory as advocated in [Chesnel, Ciarlet, T -coercivity and continuous Galerkin methods: application to transmission problems with sign changing coefficients (2013)], we propose a new variational formulation of the…
A mathematical model for an elastoplastic porous continuum subject to large strains in combination with reversible damage (aging), evolving porosity, water and heat transfer is advanced. The inelastic response is modeled within the frame of…
Variational integrators are derived for structure-preserving simulation of stochastic forced Hamiltonian systems. The derivation is based on a stochastic discrete Hamiltonian which approximates a type-II stochastic generating function for…
This paper formulates a variational approach for treating observational uncertainty and/or computational model errors as stochastic transport in dynamical systems governed by action principles under nonholonomic constraints. For this…
The paper considers the general case of incompressible non-classical elasticity with small deformations and rotations. The thermodynamic stability is analysed for free energy density with three rotational degrees of freedom. Although the…
The aim of this paper is to prove the existence of weak solution for a quasi-static evolution of thermo-visco-elastic model with Norton-Hoff law of plasticity. The dependence on temperature occurs both in the elastic constitutive equations…
A quasistatic nonlinear model for finite-strain poro-visco-elasticity is considered in the Lagrangian frame using Kelvin-Voigt rheology. The model consists of a mechanical equation which is coupled to a diffusion equation with a degenerate…
We present a numerical framework for modeling extended hyperelastic bodies based on a Lagrangian formulation of general relativistic elasticity theory. We use finite element methods to discretize the body, then use the semi--discrete action…
In this article, we present the structure-preserving discretization of linear one-dimensional port-Hamiltonian (PH) systems of two conservation laws using discontinuous Galerkin (DG) methods. We recall the DG discretization procedure which…