Volume 24, Issue 5
Recursive POD Expansion for the Advection-Diffusion-Reaction Equation

M. Azaïez, T. Chacón Rebollo, E. Perracchione & J. M. Vega

Commun. Comput. Phys., 24 (2018), pp. 1556-1578.

Published online: 2018-06

Preview Full PDF 945 2215
Export citation
  • Abstract

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.

  • Keywords

Reduced order methods, recursive POD, multivariate functions.

  • AMS Subject Headings

65D15, 65M70, 74F10

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address
  • BibTex
  • RIS
  • TXT
@Article{CiCP-24-1556, 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 = {

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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2017-0257}, url = {http://global-sci.org/intro/article_detail/cicp/12489.html} }
TY - JOUR T1 - Recursive POD Expansion for the Advection-Diffusion-Reaction Equation JO - Communications in Computational Physics VL - 5 SP - 1556 EP - 1578 PY - 2018 DA - 2018/06 SN - 24 DO - http://dor.org/10.4208/cicp.OA-2017-0257 UR - https://global-sci.org/intro/article_detail/cicp/12489.html KW - Reduced order methods, recursive POD, multivariate functions. AB -

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.

M. Azaïez, T. Chacón Rebollo, E. Perracchione & J. M. Vega. (2020). Recursive POD Expansion for the Advection-Diffusion-Reaction Equation. Communications in Computational Physics. 24 (5). 1556-1578. doi:10.4208/cicp.OA-2017-0257
Copy to clipboard
The citation has been copied to your clipboard