Reduced basis approximations for geometrically parametrized advection-diffusion equations are investigated. The parametric domains are assumed to be images of a reference domain through a piecewise polynomial map; this may lead to nonaffinely parametrized diffusion tensors that are treated with an empirical interpolation method. An a posteriori error bound including a correction term due to thi...

Numerical approximations of fractional PDEs in unbounded domains are considered in this paper. Since their solutions decay slowly with power laws at infinity, a domain truncation approach is not effective as no transparent boundary condition is available. We develop efficient Hermite-collocation and Hermite–Galerkin methods for solving a class of fractional PDEs in unbounded domains directly, a...

A finite element based level set method is proposed for structural topology optimization. Because both the level set equation and the reinitialization equation are advection dominated partial differential equations, the standard Galerkin finite element method may produce oscillating results. In this paper, both equations are solved using a streamline diffusion finite element method (SDFEM). The...

In this work we discuss the further development of the general scheme of the asymptotic method of differential inequalities to investigate stability and motion of sharp internal layers (fronts) for nonlinear singularly perturbed parabolic equations, which are called in applications reaction-diffusion-advection equations. Our approach is illustrated for some new important cases of initial bounda...

Explicit stabilized methods for stiff ordinary differential equations have a long history. Proposed in the early 1960s and developed during 40 years for the integration of stiff ordinary differential equations, these methods have recently been extended to implicit-explicit or partitioned type methods for advection-diffusion-reaction problems, and to efficient explicit solvers for stiff mean-squ...

A stochastic state space model for the estimation f fiver temperature is presented, setting the stage for its implementation in optimal control algorithms. Physical processes modeled include advection, diffusion, and environmental heat exchange; the mathematical formulation isone dimensional. The deterministic formulation uses a hybrid characteristics-finite differences numerical scheme for the...

The main purpose of this paper is to analyze the stability and error estimates of the local discontinuous Galerkin (LDG) methods coupled with carefully chosen implicit-explicit (IMEX) Runge–Kutta time discretization up to third order accuracy for solving one-dimensional linear advection-diffusion equations. In the time discretization the advection term is treated explicitly and the diffusion te...

Advection-diffusion equations arise in a number of important applications. Their robust and accurate numerical solution is – in case of advection dominated flows – still a challenge. Often it is neglected that the physical processes are governed by a velocity field u which itself is the solution of a hydrodynamical model like the incompressible Navier-Stokes equations. In this paper we address ...

In this work, a novel image-based method is presented to characterize the heat and mass transfer rates in Hele-Shaw microfluidic reactor. A Fourier transform infrared (FTIR) spectrometer used transmission mode combination with an (IR) camera simultaneously measure molar concentration thermal fields chip within few seconds. classical exothermic NaOH + HCl ? NaCl H2O chemical reaction produce mul...