Related papers: The Onsager principle and structure preserving num…
We propose fully discrete, implicit-in-time finite-volume schemes for a general family of non-linear and non-local Fokker-Planck equations with a gradient-flow structure, usually known as aggregation-diffusion equations, in any dimension.…
The main objective of this paper is to present an efficient structure-preserving scheme, which is based on the idea of the scalar auxiliary variable approach, for solving the space fractional nonlinear Schr\"{o}dinger equation. First, we…
In this paper, we introduce second order and fourth order space discretization via finite difference implementation of the finite element method for solving Fokker-Planck equations associated with irreversible processes. The proposed…
The Swift-Hohenberg equation as a central nonlinear model in modern physics has a gradient flow structure. Here we introduce fully discrete discontinuous Galerkin (DG) schemes for a class of fourth order gradient flow problems, including…
In this paper we present a numerical method for hydrodynamic models that arise from time dependent density functional theories of freezing. The models take the form of compressible Navier-Stokes equations whose pressure is determined by the…
This paper proposes a decoupled numerical scheme of the time-dependent Ginzburg--Landau equations under the temporal gauge. For the magnetic potential and the order parameter, the discrete scheme adopts the second type Ned${\rm…
Starting from the classic contraction mapping principle, we establish a general, flexible, variational setting that turns out to be applicable to many situations of existence in Differential Equations. We show its potentiality with some…
In this paper, we develop variational integrators for the nonequilibrium thermodynamics of simple closed systems. These integrators are obtained by a discretization of the Lagrangian variational formulation of nonequilibrium thermodynamics…
The construction of numerical schemes for the Kuramoto model is challenging due to the structural properties of the system which are essential in order to capture the correct physical behavior, like the description of stationary states and…
We present a new hydrodynamic model for incompressible binary fluids that is thermodynamically consistent and non-isothermal. This model follows the generalized Onsager principle and Boussinesq approximation and preserves the volume of each…
In this paper we introduce a numerical scheme which preserves the long time behavior of solutions to the Kolmogorov equation. The method presented is based on a self-similar change of variables technique to transform the Kolmogorov equation…
We present a new scheme for solving Navier-Stokes systems. This is inspired by material differentiation and combined with discrete Morse semi-flow. The solution has the first energy inequality, we set some assumption though. This result…
We introduce an efficient split finite element (FE) discretization of a y-independent (slice) model of the rotating shallow water equations. The study of this slice model provides insight towards developing schemes for the full 2D case.…
We introduce a new structure preserving, second order in time relaxation-type scheme for approximating solutions of the Schr\"odinger-Poisson system. More specifically, we use the Crank-Nicolson scheme as a time stepping mechanism, whilst…
In this note we propose a basic $L^2$-based approach for studying the global and local energy equalities of the incompressible 3D Navier-Stokes equations in the standard energy class on $\mathbb{T}^3 \times (0,T]$. Motivated by L. Onsager's…
In this paper, we consider numerical approximation of constrained gradient flows of planar closed curves, including the Willmore and the Helfrich flows. These equations have energy dissipation and the latter has conservation properties due…
In this work, we propose a numerical approach for simulations of large deformations of interfaces in a level set framework. To obtain a fast and viable numerical solution in both time and space, temporal discretization is based on the…
In this paper, we study the convergence analysis for a robust stochastic structure-preserving Lagrangian numerical scheme in computing effective diffusivity of time-dependent chaotic flows, which are modeled by stochastic differential…
A unified approach to derive optimal finite differences is presented which combines three critical elements for numerical performance especially for multi-scale physical problems, namely, order of accuracy, spectral resolution and…
In this paper, we develop an energy dissipative numerical scheme for gradient flows of planar curves, such as the curvature flow and the elastic flow. Our study presents a general framework for solving such equations. To discretize time, we…