Applications of the pseudo residual-free bubbles to the stabilization of the convection-diffusion-reaction problems in 2D

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Sendur A., Nesliturk A., Kaya A.

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, vol.277, pp.154-179, 2014 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 277
  • Publication Date: 2014
  • Doi Number: 10.1016/j.cma.2014.04.019
  • Journal Name: COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.154-179
  • Keywords: Stabilized finite element methods, Pseudo residual-free bubbles, Augmented space, FINITE-ELEMENT METHODS, COMPUTATIONAL FLUID-DYNAMICS, NAVIER-STOKES EQUATIONS, ADVECTION-DIFFUSION, RECTANGULAR GRIDS, FORMULATION, MULTISCALE, STABILITY, CHOICE, SUPG
  • Akdeniz University Affiliated: Yes

Abstract

A stabilized finite element method is studied herein for two-dimensional convection–diffusion–reaction problems. The method is based on the residual-free bubbles (RFB) method. However we replace the RFB functions by their cheap, yet efficient approximations computed on a specially chosen subgrid, which retain the same qualitative behavior. Since the correct spot of subgrid points plays a crucial role in the approximation, it is important to determine their optimal locations, which we do it through a minimization process with respect to the L1L1-norm. The resulting numerical method has similar stability features with the well-known stabilized methods in the literature for the whole range of problem parameters and this fact is also confirmed by numerical experiments.