We study the effect of the streamline upwind/Petrov Galerkin (SUPG) stabilized finite element method on the discretization of optimal control problems governed by linear advection-diffusion equations. We compare two approaches for the numerical solution of such optimal control problems. In the discretize-then-optimize approach the optimal control problem is first discretized, using the SUPG met...

We give a brief overview of stabilized finite element methods and illustrate the developments applied to the advection-diffusion equation.

in this paper, a modeling tool for risk assessment analysis of the movement of hydrocarbon contaminants in the vadose zone and mass flux of contamination release into the groundwater table was developed. also, advection-diffusion-reaction equations in combination with a three-phase equilibrium state between trapped air, soil humidity, and solid particles of unsaturated soil matrix were numerica...

Abstract: The use of the conventional advection diffusion equation in many physical situations has been questioned by many investigators in recent years and alternative diffusion models have been proposed. Fractional space derivatives are used to model anomalous diffusion or dispersion, where a particle plume spreads at a rate inconsistent with the classical Brownian motion model. When a fracti...

Mathematical and computational modeling of calcium signalling in nerve cells has produced considerable insights into how the cells contracts with other cells under the variation of biophysical and physiological parameters. The modeling of calcium signaling in astrocytes has become more sophisticated. The modeling effort has provided insight to understand the cell contraction. Main objective of ...

In the last three decades, interest in fractional calculus has experienced rapid growth and at present we can find many papers devoted its theoretical and application aspects (see the work of Machado et al. (2011) and the references therein). Fractional order models of real systems are often more adequate than the usually used integer order models in electrochemistry (Ichise et al., 1971), adve...

We present nanosecond time-scale Vlasov-Fokker-Planck-Maxwell modeling of magnetized plasma transport and dynamics in a hohlraum with an applied external magnetic field, under conditions similar to recent experiments. Self-consistent modeling of the kinetic electron momentum equation allows for a complete treatment of the heat flow equation and Ohm's law, including Nernst advection of magnetic ...

We consider a prototype two-phase uid-ow model with capillary forces. The pressure equation is solved using standard nite-elements and multigrid techniques. The parabolic saturation equation is addressed via a novel corrected operator splitting approach. In typical applications, the importance of advection versus diiusion (capillary forces) may change rapidly during a simulation. The corrected ...