相关论文: Energy preserving moving mesh methods applied to t…
Many practical problems can be described by second-order system $\ddot{q}=-M\nabla U(q)$, in which people give special emphasis to some invariants with explicit physical meaning, such as energy, momentum, angular momentum, etc. However,…
We show that, under suitable conditions, finite-dimensional systems describing invariant solutions of partial differential equations (PDEs) inherit local Hamiltonian operators through the mechanism of invariant reduction, which applies…
The backward Euler-Maruyama (BEM) method is employed to approximate the invariant measure of stochastic differential equations, where both the drift and the diffusion coefficient are allowed to grow super-linearly. The existence and…
We introduce a family of fourth order two-step methods that preserve the energy function of canonical polynomial Hamiltonian systems. Each method in the family may be viewed as a correction of a linear two-step method, where the correction…
We consider the design of structure-preserving discretization methods for the solution of systems of boundary controlled Partial Differential Equations (PDEs) thanks to the port-Hamiltonian formalism. We first provide a novel general…
The study of the long time conservation for numerical methods poses interesting and challenging questions from the point of view of geometric integration. In this paper, we analyze the long time energy and magnetic moment conservations of…
A conforming finite element scheme with mixed explicit-implicit time discretization for quasi-incompressible Navier-Stokes-Maxwell-Stefan systems in a bounded domain with periodic boundary conditions is presented. The system consists of the…
In this paper, we consider the numerical methods preserving single or multiple conserved quantities, and these methods are able to reach high order of strong convergence simultaneously based on some kinds of projection methods. The…
Recently, a new family of integrators (Hamiltonian Boundary ValueMethods) has been introduced, which is able to precisely conserve the energy function of polynomial Hamiltonian systems and to provide a practical conservation of the energy…
This paper is devoted to the numerical analysis of a fully discrete finite element approximation for the stochastic Benjamin-Bona-Mahony equation driven by multiplicative noise. We first establish the existence and uniqueness of solutions…
A finite element discretization using a method of lines approached is proposed for approximately solving the Poisson-Nernst-Planck (PNP) equations. This discretization scheme enforces positivity of the computed solutions, corresponding to…
Direct observations of compact objects, in the form of radiation spectra, gravitational waves from VIRGO/LIGO, and forthcoming direct imaging, are currently one of the primary source of information on the physics of plasmas in extreme…
A moving mesh finite element method is studied for the numerical solution of Bernoulli free boundary problems. The method is based on the pseudo-transient continuation with which a moving boundary problem is constructed and its steady-state…
In the second part of this series, we use the Lagrange multiplier approach proposed in the first part \cite{CheS21} to construct efficient and accurate bound and/or mass preserving schemes for a class of semi-linear and quasi-linear…
A novel structure-preserving numerical method to solve random hyperbolic systems of conservation laws is presented. The method uses a concept of generalized, measure-valued solutions to random conservation laws. This yields a linear partial…
From the energy-momentum tensors of the electromagnetic field and the mechanical energy-momentum, the equations of energy conservation and balance of electromagnetic and mechanical forces are obtained. The equation for the Abraham force in…
This work surveys an r-adaptive moving mesh finite element method for the numerical solution of premixed laminar flame problems. Since the model of chemically reacting flow involves many different modes with diverse length scales, the…
Wereportonanewmultiscalemethodapproachforthestudyofsystemswith wide separation of short-range forces acting on short time scales and long-range forces acting on much slower scales. We consider the case of the Poisson-Boltzmann equation that…
We propose a moving mesh adaptive approach for solving time-dependent partial differential equations. The motion of spatial grid points is governed by a moving mesh PDE (MMPDE) in which a mesh relaxation time \tau is employed as a…
We present two novel classes of fully discrete energy-preserving algorithms for the sine-Gordon equation subject to Neumann boundary conditions. The cosine pseudo-spectral method is first used to develop structure-preserving spatial…