Adaptive discontinuous Galerkin methods for non-linear diffusion-convection-reaction equations

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UZUNCA M., KARASÖZEN B., Manguoglu M.

COMPUTERS & CHEMICAL ENGINEERING, vol.68, pp.24-37, 2014 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 68
  • Publication Date: 2014
  • Doi Number: 10.1016/j.compchemeng.2014.05.002
  • Journal Name: COMPUTERS & CHEMICAL ENGINEERING
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.24-37
  • Keywords: Non-linear diffusion-convection reaction, Discontinuous Galerkin, Adaptivity, Matrix reordering, Preconditioning, FINITE-ELEMENT METHODS, PRECONDITIONERS, APPROXIMATION, NONSTATIONARY, ALGORITHM
  • Middle East Technical University Affiliated: Yes

Abstract

In this work, we apply the adaptive discontinuous Galerkin (DGAFEM) method to the convection dominated non-linear, quasi-stationary diffusion convection reaction equations. We propose an efficient preconditioner using a matrix reordering scheme to solve the sparse linear systems iteratively arising from the discretized non-linear equations. Numerical examples demonstrate effectiveness of the DGAFEM to damp the spurious oscillations and resolve well the sharp layers occurring in convection dominated non-linear equations. (C) 2014 Elsevier Ltd. All rights reserved.