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A boundary element numerical scheme for the two‐dimensional convection–diffusion equation
Author(s) -
Romero Luis M.,
Benitez Francisco G.
Publication year - 2008
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.2391
Subject(s) - discretization , scheme (mathematics) , mathematics , convection–diffusion equation , boundary element method , numerical solution of the convection–diffusion equation , finite element method , boundary value problem , boundary (topology) , numerical analysis , mathematical analysis , mixed finite element method , physics , thermodynamics
In this study, the theoretical and numerical fundamentals of BIEM techniques for the two‐dimensional convection–diffusion problem are presented. After an extended presentation of the basic integral formulation, the discretizing and iterative processes for its resolution are introduced. Interesting remarks on general expressions versus previously published particularized results are worth mentioning. A numerical solution scheme is provided, which has been completely developed and designed to the physical problem posed. A novel scheme based in the simultaneous solving of the potential and the gradient of the potential boundary integral equations is included. A diversity of problems is tested to prove the possibilities of the method. Copyright © 2008 John Wiley & Sons, Ltd.