Analysis of a new stabilized finite element method for the reaction-convection-diffusion equations with a large reaction coefficient

Please use this identifier to cite or link to this item: https://ir.lib.ncu.edu.tw/handle/987654321/109152

Title:	Analysis of a new stabilized finite element method for the reaction-convection-diffusion equations with a large reaction coefficient
Authors:	楊肅煜;Duan, Huo-Yuan;Hsieh, Po-Wen;Tan, Roger C.E.;Yang, Suh-Yuh
Contributors:	理學院數學系
Keywords:	Approximation;Boundary layer;Coefficients;Computational methods in fluid dynamics;Convection and heat transfer;Diffusivity;Errors;Exact sciences and technology;Finite element method;Fluid dynamics;Fundamental areas of phenomenology (including applications);Interior layer;Mathematical analysis;Mathematics;Norms;Partial differential equations;Peclet number;Physics;Reaction–convection–diffusion equation;Sciences and techniques of general use;Stabilization method;Turbulence simulation and modeling;Turbulent flows, convection, and heat transfer
Date:	2012-11-01
Issue Date:	2026-04-23 16:10:45 (UTC+8)
Publisher:	Elsevier;Kidlington: Elsevier B.V
Abstract:	摘要： In this paper, we propose and analyze a new stabilized finite element method using continuous piecewise linear (or bilinear) elements for solving 2D reaction–convection–diffusion equations. The equation under consideration involves a small diffusivity ε and a large reaction coefficient σ, leading to high Péclet number and high Damköhler number. In addition to giving error estimates of the approximations in L2 and H1 norms, we explicitly establish the dependence of error bounds on the diffusivity, the L∞ norm of convection field, the reaction coefficient and the mesh size. Our analysis shows that the proposed method is particularly suitable for problems with a small diffusivity and a large reaction coefficient, or more precisely, with a large mesh Péclet number and a large mesh Damköhler number. Several numerical examples exhibiting boundary or interior layers are given to illustrate the high accuracy and stability of the proposed method. The results obtained are also compared with those of existing stabilization methods. 出版者： Kidlington: Elsevier B.V 出版日期： 2012-11-01 出處： Computer methods in applied mechanics and engineering, 2012-11, Vol.247-248, p.15-36 資源來源： ScienceDirect 版權： 2012 Elsevier B.V. 版權： 2015 INIST-CNRS 識別號： ISSN: 0045-7825 識別號： EISSN: 1879-2138 識別號： DOI: 10.1016/j.cma.2012.07.018 識別號： CODEN: CMMECC
Appears in Collections:	[Department of Mathematics] journal & Dissertation

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