Solving of the coefficient inverse problems for a nonlinear singularly perturbed reaction-diffusion-advection equation with the final time data

D. V. Lukyanenko, M. A. Shishlenin, V. T. Volkov

Research output: Contribution to journalArticlepeer-review

20 Citations (Scopus)

Abstract

We propose the numerical method for solving coefficient inverse problem for a nonlinear singularly perturbed reaction-diffusion-advection equation with the final time observation data based on the asymptotic analysis and the gradient method. Asymptotic analysis allows us to extract a priory information about interior layer (moving front), which appears in the direct problem, and boundary layers, which appear in the conjugate problem. We describe and implement the method of constructing a dynamically adapted mesh based on this a priory information. The dynamically adapted mesh significantly reduces the complexity of the numerical calculations and improve the numerical stability in comparison with the usual approaches. Numerical example shows the effectiveness of the proposed method.

Original languageEnglish
Pages (from-to)233-247
Number of pages15
JournalCommunications in Nonlinear Science and Numerical Simulation
Volume54
DOIs
Publication statusPublished - 1 Jan 2018

Keywords

  • Coefficient inverse problem
  • Dynamically adapted mesh
  • Final time observed data
  • Interior and boundary layers
  • Reaction-diffusion-advection equation
  • Singularly perturbed problem
  • BURGERS-EQUATION

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