• Corpus ID: 118295519

Parabolic inverse convection-diffusion-reaction problem solved using an adaptive parametrization

@article{Deolmi2011ParabolicIC,
  title={Parabolic inverse convection-diffusion-reaction problem solved using an adaptive parametrization},
  author={Giulia Deolmi and Fabio Marcuzzi},
  journal={arXiv: Numerical Analysis},
  year={2011}
}
This paper investigates the solution of a parabolic inverse problem based upon the convection-diffusion-reaction equation, which can be used to estimate both water and air pollution. We will consider both known and unknown source location: while in the first case the problem is solved using a projected damped Gauss-Newton, in the second one it is ill-posed and an adaptive parametrization with time localization will be adopted to regularize it. To solve the optimization loop a model reduction… 

References

SHOWING 1-10 OF 32 REFERENCES

An inverse source problem for the convection‐diffusion equation

Purpose – To develop a numerical technique for solving the inverse source problem associated with the constant coefficients convection‐diffusion equation.Design/methodology/approach – The proposed

Optimal control of the convection-diffusion equation using stabilized finite element methods

A stabilization scheme which leads to improved approximate solutions even on corse meshes in the convection dominated case and the in general different approaches “optimize-then- discretize” and "discretize- then-optimize" coincide for the proposed discretization scheme.

An Inverse Convection Problem

The nature of inverse problems in convective environments is investigated. The illposed quality inherent in inverse problems is verified for free convection laminar flow in a vertical channel. A

Identification of point sources in two-dimensional advection-diffusion-reaction equation: application to pollution sources in a river. Stationary case

We consider the problem of determining pollution sources in a river by using boundary measurements. The mathematical model is a two-dimensional advection-diffusion-reaction equation in the stationary

Distributed and Boundary Control of Singularly Perturbed Advection-Diffusion-Reaction Problems

We consider the numerical analysis of quadratic optimal control problems with distributed and Robin boundary control governed by an elliptic problem. The Galerkin discretization is stabilized via the

A sequential method of solving inverse natural convection problems

A sequential algorithm is developed to solve an inverse natural convection problem of estimating the time-varying strength of a heat source from the knowledge of temperature readings taken inside the

Analysis of the Streamline Upwind/Petrov Galerkin Method Applied to the Solution of Optimal Control Problems ∗

Estimates for the error between the solution of the infinite dimensional optimal control problem and their approximations computed using the previous approaches are presented and prove that the optimize-then-discretize approach has better asymptotic convergence properties if finite elements of order greater than one are used.