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A stabilized mixed finite element method for the first‐order form of advection–diffusion equation
Author(s) -
Masud Arif,
Kwack JaeHyuk
Publication year - 2008
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.1842
Subject(s) - finite element method , polygon mesh , scale (ratio) , benchmark (surveying) , advection , mathematics , stability (learning theory) , diffusion , mixed finite element method , mathematical optimization , mathematical analysis , computer science , geometry , physics , thermodynamics , geology , geodesy , quantum mechanics , machine learning
This paper presents a stabilized mixed finite element method for the first‐order form of advection–diffusion equation. The new method is based on an additive split of the flux‐field into coarse‐ and fine‐scale components that systematically lead to coarse and fine‐scale variational formulations. Solution of the fine‐scale variational problem is mathematically embedded in the coarse‐scale problem and this yields the resulting method. A key feature of the method is that the characteristic length scale of the mesh does not appear explicitly in the definition of the stability parameter that emerges via the solution of the fine‐scale problem. The new method yields a family of equal‐ and unequal‐order elements that show stable response on structured and unstructured meshes for a variety of benchmark problems. Copyright © 2008 John Wiley & Sons, Ltd.