@Article{CiCP-24-5,
author = {},
title = {Recursive POD Expansion for the Advection-Diffusion-Reaction Equation},
journal = {Communications in Computational Physics},
year = {2018},
volume = {24},
number = {5},
pages = {1556--1578},
abstract = {<p style="text-align: justify;">This paper deals with the approximation of advection-diffusion-reaction
equation solution by reduced order methods. We use the Recursive POD approximation
for multivariate functions introduced in [5] and applied to the low tensor representation
of the solution of the reaction-diffusion partial differential equation. In this
contribution we extend the Recursive POD approximation for multivariate functions
with an arbitrary number of parameters, for which we prove general error estimates.
The method is used to approximate the solutions of the advection-diffusion-reaction
equation. We prove spectral error estimates, in which the spectral convergence rate
depends only on the diffusion interval, while the error estimates are affected by a factor
that grows exponentially with the advection velocity, and are independent of the
reaction rate if this lives in a bounded set. These error estimates are based upon the
analyticity of the solution of these equations as a function of the parameters (advection
velocity, diffusion, reaction rate). We present several numerical tests, strongly consistent
with the theoretical error estimates.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.OA-2017-0257},
url = {https://global-sci.com/article/80001/recursive-pod-expansion-for-the-advection-diffusion-reaction-equation}
}