# 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

- Mathematics, Physics
- 2006

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

- Computer Science, MathematicsNumerische Mathematik
- 2007

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

- Mathematics
- 1989

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

- Mathematics
- 2007

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

- Mathematics
- 2009

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 functional optimization formulation and implementation of an inverse natural convection problem

- Mathematics
- 1997

### A sequential method of solving inverse natural convection problems

- Mathematics
- 2002

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 ∗

- Mathematics, Computer Science
- 2002

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.

### Inverse reactive transport simulator (INVERTS): an inverse model for contaminant transport with nonlinear adsorption and source terms

- MathematicsEnviron. Model. Softw.
- 2001