相关论文: Unconditionally energy stable fully discrete schem…
In this paper we present two unconditionally energy stable finite difference schemes for the Modified Phase Field Crystal (MPFC) equation, a sixth-order nonlinear damped wave equation, of which the purely parabolic Phase Field Crystal (PFC)…
This paper proposes a second-order accurate numerical scheme for the Patlak-Keller-Segel system with various mobilities for the description of chemotaxis. Formulated in a variational structure, the entropy part is novelly discretized by a…
In this paper, we present and analyze an energy-conserving and linearly implicit scheme for solving the nonlinear wave equations. Optimal error estimates in time and superconvergent error estimates in space are established without time-step…
This work studies the chemotaxis-haptotaxis system $$\left\{ \begin{array}{ll} u_t= \Delta u - \chi \nabla \cdot (u\nabla v) - \xi \nabla \cdot (u\nabla w) + \mu u(1-u-w), &\qquad x\in \Omega, \, t>0, \\[1mm] v_t=\Delta v-v+u, &\qquad x\in…
In this article we develop a fully discrete variational scheme that approximates the equations of three dimensional elastodynamics with polyconvex stored energy. The fully discrete scheme is based on a time-discrete variational scheme…
We apply the finite element cell-centered (FECC) scheme [2] to the solution of the nearly incompressible elasticity problem. By applying a technique of dual mesh, such a low-order finite element scheme can be constructed from any given mesh…
In this paper, we propose energy-conserving numerical schemes for the Vlasov-Amp\`{e}re (VA) systems. The VA system is a model used to describe the evolution of probability density function of charged particles under self consistent…
In this paper, we present energy-stable numerical schemes for a Smectic-A liquid crystal model. This model involve the hydrodynamic velocity-pressure macroscopic variables $({\bf u},p)$ and the microscopic order parameter of Smectic-A…
This paper develops and analyzes an optimal-order semi-discrete scheme and its fully discrete finite element approximation for nonlinear stochastic elastic wave equations with multiplicative noise. A non-standard time-stepping scheme is…
We consider a system of nonlinear partial differential equations describing the motion of an incompressible chemically reacting generalized Newtonian fluid in three space dimensions. The governing system consists of a steady…
In this work, we develop novel structure-preserving numerical schemes for a class of nonlinear Fokker--Planck equations with nonlocal interactions. Such equations can cover many cases of importance, such as porous medium equations with…
For the classical zero-flux chemotaxis-consumption model \begin{equation*} u_t= \Delta u - \chi \nabla \cdot (u \nabla v) \quad \textrm{and}\quad v_t=\Delta v- uv, \quad \text{ with } (x,t)\in \Omega \times (0,T_{max}), \end{equation*}…
We present a novel second-order semi-implicit hybrid finite volume / finite element (FV/FE) scheme for the numerical solution of the incompressible and weakly compressible Navier-Stokes equations on moving unstructured meshes using an…
We present a novel framework based on semi-bounded spatial operators for analyzing and discretizing initial boundary value problems on moving and deforming domains. This development extends an existing framework for well-posed problems and…
This paper deals with the quasilinear fully parabolic attraction-repulsion chemotaxis system \begin{align*} u_t=\nabla \cdot (D(u)\nabla u) -\nabla \cdot (G(u)\chi(v)\nabla v) +\nabla\cdot(H(u)\xi(w)\nabla w), \quad v_t=d_1\Delta v+\alpha…
This work investigates the design and analysis of energy-decay preserving numerical schemes for Maxwell's equations in a Cole-Cole (C-C) dispersive medium. A continuous energy-decay law is first established for the C-C model through a…
In density-based topology optimization, design variables associated to the boundaries of the design domain require unique treatment to negate boundary effects arising from the filtering technique. An effective approach to deal with…
An implicit Euler finite-volume scheme for a spinorial matrix drift-diffusion model for semiconductors is analyzed. The model consists of strongly coupled parabolic equations for the electron density matrix or, alternatively, of weakly…
We propose and analyze the numerical approximation for a viscoelastic Euler-Bernoulli beam model containing a nonlinear strong damping coefficient. The finite difference method is used for spatial discretization, while the backward Euler…
We construct a decoupled, first-order, fully discrete, and unconditionally energy stable scheme for the Cahn-Hilliard-Navier-Stokes equations. The scheme is divided into two main parts. The first part involves the calculation of the…