We present a new family of stabilized methods for the Stokes problem. The focus of the paper is on the lowest order velocity-pressure pairs. While not LBB compliant, their simplicity and attractive computational properties make these pairs a popular choice in engineering practice. Our stabilization approach is motivated by terms that characterize the LBB 'deficiency' of the unstable spaces. The stabilized methods are defined by using these terms to modify the saddle-point Lagrangian associated with the Stokes equations. The new stabilized methods offer a number of attractive computational properties. In contrast to other stabilization procedures, they are parameter free, do not require calculation of higher order derivatives or edge-based data structures, and always lead to symmetric linear systems. Furthermore, the new methods are unconditionally stable, achieve optimal accuracy with respect to solution regularity, and have simple and straightforward implementations. We present numerical results in two and three dimensions that showcase the excellent stability and accuracy of the new methods.

Stabilization of low-order mixed finite elements for the stokes equations.

https://bxscience.enschool.org/ourpages/auto/2014/9/5/42400025/Example%209.pdf

Applications of artificial neural networks for thermal analysis of heat exchangers – A review

The threshold of a stochastic SIRS epidemic model with saturated incidence

Applications of ANNs in flow and heat transfer problems in nuclear engineering: A review work

This paper discusses a generalized time-varying SEIR propagation disease model subject to delays which potentially involves mixed regular and impulsive vaccination rules. The model takes also into account the natural population growing and the mortality associated to the disease, and the potential presence of disease endemic thresholds for both the infected and infectious population dynamics as well as the lost of immunity of newborns. The presence of outsider infectious is also considered. It is assumed that there is a finite number of time-varying distributed delays in the susceptible-infected coupling dynamics influencing the susceptible and infected differential equations. It is also assumed that there are time-varying point delays for the susceptible-infected coupled dynamics influencing the infected, infectious, and removed-by-immunity differential equations. The proposed regular vaccination control objective is the tracking of a prescribed suited infectious trajectory for a set of given initial conditions. The impulsive vaccination can be used to improve discrepancies between the SEIR model and its suitable reference one.

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On a Generalized Time-Varying SEIR Epidemic Model with Mixed Point and Distributed Time-Varying Delays and Combined Regular and Impulsive Vaccination Controls

Huiming Wei

Papers

Analysis of a saturation incidence SVEIRS epidemic model with pulse and two time delays

Global attractivity and permanence of a SVEIR epidemic model with pulse vaccination and time delay

Global attractivity and permanence of a delayed SVEIR epidemic model with pulse vaccination and saturation incidence

Study on the characteristic points of boiling curve by using wavelet analysis and genetic neural network

Study on the onset of nucleate boiling in narrow annular channel by genetic neural network