In this paper, we propose for the first time a linearly coupled, energy stable scheme for the Navier–Stokes– Cahn–Hilliard system with generalized Navier boundary condition. We rigorously prove the unconditional energy stability for the proposed time discretization as well as for a fully discrete finite element scheme. Using numerical tests, we verify the accuracy, confirm the decreasing proper...

We propose and analyze a partitioned numerical method for the fully evolutionary Stokes-Darcy equations that model the coupling between surface and groundwater flows. The proposed method uncouples the surface from the groundwater flow by using the implicit-explicit combination of the Crank-Nicolson and Leapfrog methods for the discretization in time with added stabilization terms. We prove that...

In this paper, a highly accurate parallel difference scheme for the fourth-order diffusion equation is studied. Based on a group of new Saul’yev type asymmetric difference schemes, a high-order, unconditionally stable and parallel alternating group explicit scheme is derived. The scheme is fourth-order truncation error in space, which is much more accurate than the known methods. Numerical expe...

This paper is concerned with accurate and efficient numerical methods for solving viscous and nonviscous wave problems. The paper first introduces a new second-order PR-ADI like scheme. For an efficient simulation, the scheme is also extended to a highorder compact PRADI likemethod. Both of them have the advantages of unconditional stability, less impact of the perturbing terms on the accuracy,...

We study in this paper two linearized backward Euler schemes with Galerkin finite element approximations for the time-dependent nonlinear Joule heating equations. By introducing a time-discrete (elliptic) system as proposed in Li and Sun (Int J Numer Anal Model 10:622–633, 2013; SIAM J Numer Anal (to appear)), we split the error function as the temporal error function plus the spatial error fun...

This work describes a projection method for approximating incompressible viscous 1ows of nonuniform density. It is shown that unconditional stability in time is possible provided two projections are performed per time step. A 3nite element implementation and a 3nite volume one are described and compared. The performance of the two methods are tested on a Rayleigh–Taylor instability. We show tha...

A novel integration scheme for nonlinear dynamics of geometrically exact shells is developed based on the inextensible director assumption. The new algorithm is designed so as to imply the strict decay of the system total mechanical energy at each time step, and consequently unconditional stability is achieved in the nonlinear regime. Furthermore, the scheme features tunable high frequency nume...

This paper deals with numerical solution to the multi-term time fractional diffusion equation in a finite domain. An implicit finite difference scheme is established based on Caputo’s definition to the fractional derivatives, and the upper and lower bounds to the spectral radius of the coefficient matrix of the difference scheme are estimated, with which the unconditional stability and converge...

Key properties of the box scheme are shown to be advantageous for reactive flow problems. Unconditional stability and compact conservation are shown by a detailed modified equation analysis to enable the scheme to reflect exactly the “reduced speed,” enhanced diffusion, and dispersion which are typical of such “hyperbolic conservation laws with relaxation.” A novel modified equation analysis is...

We study a dynamic equilibrium model in which agents have adaptive expectations and monetary authorities pursue an inflation target. We show how alternative monetary stabilization policies become more effective when fiscal constraints on deficits are implemented, although they are not binding at the equilibrium target. In particular, we show that the inflation target equilibrium can be locally,...