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In this paper, we propose a decoupled stabilized finite element method for the time–dependent Navier–Stokes/Biot problem by using the lowest equal‐order finite elements. The coupling problem is divided into two subproblems which can be solved in parallel: One is the Navier–Stokes model by treating the nonlinear term explicitly, and the other is the Biot model. In the numerical scheme, we use the implicit backward Euler method in time, while treat the coupling terms explicitly. The stability analysis and error estimates are established for the proposed fully discrete scheme. Numerical results are provided to justify the theory. [ABSTRACT FROM AUTHOR]

A class of nonlinear Fokker–Planck equations with nonlocal interactions may include many important cases, such as porous medium equations with external potentials and aggregation–diffusion models. The trajectory equation of the Fokker–Plank equation can be derived based on an energetic variational approach. A structure‐preserving numerical scheme that is mass conservative, energy stable, uniquely solvable, and positivity preserving at a theoretical level has also been designed in the previous work. Moreover, the numerical scheme is shown to satisfy the discrete energetic dissipation law and preserve steady states and has been observed to be second order accurate in space and first‐order accurate time in various numerical experiments. In this work, we give the rigorous convergence analysis for the highly nonlinear numerical scheme. A careful higher order asymptotic expansion is needed to handle the highly nonlinear nature of the trajectory equation. In addition, two step error estimates (a rough estimate and a refined estimate) are necessary in the convergence proof. Different from a standard error estimate, the rough estimate is performed to control the nonlinear term. A few numerical results are also presented to verify the optimal convergence order and the preservation of equilibria. [ABSTRACT FROM AUTHOR]

In this letter, two time delay dynamic models, a Time Delay Dynamical–Novel Coronavirus Pneumonia (TDD‐NCP) model and Fudan‐Chinese Center for Disease Control and Prevention (CCDC) model, are introduced to track the data of Coronavirus Disease 2019 (COVID‐19). The TDD‐NCP model was developed recently by Chengąŕs group in Fudan and Shanghai University of Finance and Economics (SUFE). The TDD‐NCP model introduced the time delay process into the differential equations to describe the latent period of the epidemic. The Fudan‐CDCC model was established when Wenbin Chen suggested to determine the kernel functions in the TDD‐NCP model by the public data from CDCC. By the public data of the cumulative confirmed cases in different regions in China and different countries, these models can clearly illustrate that the containment of the epidemic highly depends on early and effective isolations. [ABSTRACT FROM AUTHOR]

This paper concerns new continuum phenomenological model for epitaxial thin-film growth with three different forms of the Ehrlich-Schwoebel current. Two of these forms were first proposed by Politi and Villain 1996 and then studied by Evans, Thiel, and Bartelt 2006. The other one is completely new. Energy structure and properties of the new model are studied. Following the techniques used in Li and Liu 2003, we present rigorous analysis of the well-posedness, regularity, and time stability for the new model. We also studied both the global and the local behavior of the surface roughness in the growth process. By using a convex-concave time-splitting scheme, one can naturally build unconditionally stable semi-implicit numerical discretizations with linear implicit parts, which is much easier to implement than conventional models requiring nonlinear implicit parts. Despite this fundamental difference in the model, numerical experiments show that the nonlinear morphological instability of the new model agrees well with results of other models published before which indicates that the new model correctly captures the essential morphological states in the thin-film growth process. Copyright © 2017 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The energy-conserved splitting finite-difference time-domain (EC-S-FDTD) method has recently been proposed to solve the Maxwell equations with second order accuracy while numerically keep the L2 energy conservation laws of the equations. In this paper, the EC-S-FDTD scheme for the 3D Maxwell equations is proved to be energy-conserved and unconditionally stable in the discrete H1 norm. The EC-S-FDTD scheme is of second-order accuracy both in time step and spatial steps, which suggests the super-convergence of this scheme in the discrete H1 norm. And the divergence of the electric field of the EC-S-FDTD scheme in the discrete L2 norm is second-order accurate. Numerical experiments confirm our theoretical analysis. Copyright © 2012 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]