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Calcolo

, 55:27 | Cite as

A stabilizing augmented grid for rectangular discretizations of the convection–diffusion–reaction problems

  • Ali Sendur
Article
  • 68 Downloads

Abstract

We propose a numerical method for approximate solution of the convection–diffusion–reaction problems in the case of small diffusion. The method is based on the standard Galerkin finite element method on an extended space defined on the original grid plus a subgrid, where the original grid consists of rectangular elements. On each rectangular elements, we construct a subgrid with few points whose locations are critical for the stabilization of the problem, therefore they are chosen specially depending on some specific conditions that depend on the problem data. The resulting subgrid is combined with the initial coarse mesh, eventually, to solve the problem in the framework of Galerkin method on the augmented grid. The results of the numerical experiments confirm that the proposed method shows similar stability features with the well-known stabilized methods for the critical range of problem parameters.

Keywords

Stabilized finite element method Convection–diffusion–reaction problem Augmented grids 

Mathematics Subject Classification

65N30 65N50 76M10 

Supplementary material

10092_2018_269_MOESM1_ESM.pdf (737 kb)
Supplementary material 1 (pdf 737 KB)

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Copyright information

© Istituto di Informatica e Telematica del Consiglio Nazionale delle Ricerche 2018

Authors and Affiliations

  1. 1.Department of MathematicsAlanya Alaaddin Keykubat UniversityAntalyaTurkey

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