Related papers: A minimizing-movements approach to GENERIC systems
We introduce in this paper two time discretization schemes tailored for a range of Wasserstein gradient flows. These schemes are designed to preserve mass, positivity and to be uniquely solvable. In addition, they also ensure energy…
Numerical methods that preserve geometric invariants of the system, such as energy, momentum or the symplectic form, are called geometric integrators. Variational integrators are an important class of geometric integrators. The general idea…
This paper is part of a program to combine a staggered time and staggered spatial discretization of continuum mechanics problems so that any property of the continuum that is proved using vector calculus can be proven in an analogous way…
We consider a numerical scheme for Hamilton-Jacobi equations based on a direct discretization of the Lax-Oleinik semi-group. We prove that this method is convergent with respect to the time and space stepsizes provided the solution is…
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…
In the context of Discontinuous Galerkin methods, we study approximations of nonlinear variational problems associated with convex energies. We propose element-wise nonconforming finite element methods to discretize the continuous…
We study higher-order space-time variational discretisations for modeling complex processes in porous media that include fluid and structure interactions which are of fundamental importance in many engineering fields with applications in…
Introduction of renewable generation leads to significant reduction of inertia in power system, which deteriorates the quality of frequency control. This paper suggests a new control scheme utilizing controllable load to deal with low…
This article performs a unified convergence analysis of a variety of numerical methods for a model of the miscible displacement of one incompressible fluid by another through a porous medium. The unified analysis is enabled through the…
We reconsider the non-equilibrium dynamics of closed quantum systems. In particular we focus on the thermalization of integrable systems. Here we show how the generalized Gibbs Ensemble (GGE) can be constructed as the best approximation to…
Differential flatness serves as a powerful tool for controlling continuous time nonlinear systems in problems such as motion planning and trajectory tracking. A similar notion, called difference flatness, exists for discrete-time systems.…
The dynamic damage model in viscoelastic materials in Kelvin-Voigt rheology is discretised by a scheme which is coupled, suppresses spurious numerical attenuation during vibrations, and has a variational structure with a convex potential…
The control of ensembles of dynamical systems is an intriguing and challenging problem, arising for example in quantum control. We initiate the investigation of optimal control of ensembles of discrete-time systems, focusing on minimising…
We introduce the concept of volume term adaptivity for high-order discontinuous Galerkin (DG) schemes solving time-dependent partial differential equations. Termed v-adaptivity, we present a novel general approach that exchanges the…
We present a linear, second order fully discrete numerical scheme on a staggered grid for a thermodynamically consistent hydrodynamic phase field model of binary compressible fluid flow mixtures derived from the generalized Onsager…
Control laws for continuous-time dynamical systems are most often implemented via digital controllers using a sample-and-hold technique. Numerical discretization of the continuous system is an integral part of subsequent analysis. Feedback…
We consider the simulation of barotropic flow of gas in long pipes and pipe networks. Based on a Hamiltonian reformulation of the governing system, a fully discrete approximation scheme is proposed using mixed finite elements in space and…
A novel space-time discretization for the (linear) scalar-valued dissipative wave equation is presented. It is a structured approach, namely, the discretization space is obtained tensorizing the Virtual Element (VE) discretization in space…
Many differential equations with physical backgrounds are described as gradient systems, which are evolution equations driven by the gradient of some functionals, and such problems have energy conservation or dissipation properties. For…
We propose a time discretization scheme for a class of ordinary differential equations arising in simulations of fluid/particle flows. The scheme is intended to work robustly in the lubrication regime when the distance between two particles…