相关论文: Time discretization of a nonlocal phase-field syst…
This article deals with a nonlocal Penrose-Fife type phase field system with inertial term. We do not know whether we can prove existence of solutions in reference to Colli--Grasselli--Ito [Electron. J. Differential Equations 2002, No. 100,…
This article deals with a simultaneous abstract evolution equation. This includes a parabolic-hyperbolic phase-field system as an example which consists of a parabolic equation for the relative temperature coupled with a semilinear damped…
In this paper we deal with an abstract problem which includes the linearized equations of coupled sound and heat flow as an example. Recently, a time discretization of a simultaneous abstract evolution equation applying to some…
This paper deals with the nonlinear phase field system \begin{equation*} \begin{cases} \partial_t (\theta +\ell \varphi) - \Delta\theta = f & \mbox{in}\ \Omega\times(0, T), \\[1mm] \partial_t \varphi - \Delta\varphi + \xi + \pi(\varphi) =…
In this paper we deal with a singular nonlocal phase field system with inertial term. The system has the logarithm of the absolute temperature $\theta$ under time derivative. Although the system has a difficult mathematical point caused by…
A new time discretization scheme for the numerical simulation of two-phase flow governed by a thermodynamically consistent diffuse interface model is presented. The scheme is consistent in the sense that it allows for a discrete in time…
A class of abstract nonlinear time-periodic evolution problems is considered which arise in electrical engineering and other scientific disciplines. An efficient solver is proposed for the systems arising after discretization in time based…
In this paper we propose a time discretization of a system of two parabolic equations describing diffusion-driven atom rearrangement in crystalline matter. The equations express the balances of microforces and microenergy; the two phase…
We consider partial differential equations on networks with a small parameter $\epsilon$, which are hyperbolic for $\epsilon>0$ and parabolic for $\epsilon=0$. With a combination of an $\epsilon$-expansion and Runge-Kutta schemes for…
This paper develops a high-accuracy algorithm for time fractional wave problems, which employs a spectral method in the temporal discretization and a finite element method in the spatial discretization. Moreover, stability and convergence…
We construct a space-time parallel method for solving parabolic partial differential equations by coupling the Parareal algorithm in time with overlapping domain decomposition in space. The goal is to obtain a discretization consisting of…
This work aims to construct an efficient and highly accurate numerical method to address the time singularity at $t=0$ involved in a class of time-fractional parabolic integro-partial differential equations in one and two dimensions. The…
We propose a discretization of vector fields that are Hamiltonian up to multiplication by a positive function on the phase space that may be interpreted as a time reparametrization. We prove that our method is structure preserving in the…
We construct four variants of space-time finite element discretizations based on linear tensor-product and simplex-type finite elements. The resulting discretizations are continuous in space, and continuous or discontinuous in time. In a…
We analyze the method for calculation of properties of non-relativistic quantum systems based on exact diagonalization of space-discretized short-time evolution operators. In this paper we present a detailed analysis of the errors…
We present a unified framework for the analysis of space-time methods based on Galerkin-type time discretizations for parabolic and hyperbolic problems. Crucially, the stability analysis relies on a suitable choice of test functions to…
This paper deals with a nonlocal model for a hyperbolic phase field system coupling the standard energy balance equation for temperature with a dynamic for the phase variable: the latter includes an inertial term and a nonlocal…
This article considers the error analysis of finite element discretizations and adaptive mesh refinement procedures for nonlocal dynamic contact and friction, both in the domain and on the boundary. For a large class of parabolic…
In this paper, we consider a nonlinear PDE system governed by a parabolic heat equation coupled in a nonlinear way with a hyperbolic momentum equation describing the behavior of a displacement field coupled with a nonlinear elliptic…
In this paper, the problem of non-fragile finite-time stabilization for linear discrete mean-field stochastic systems is studied. The uncertain characteristics in control parameters are assumed to be random satisfying the Bernoulli…