TY - JOUR
T1 - A multiscale/stabilized finite element method for the advection-diffusion equation
AU - Masud, A.
AU - Khurram, R. A.
N1 - Funding Information:
Support for this work was provided by the ONR grant N00014-02-1-0143. This support is gratefully acknowledged. The authors wish to thank the anonymous reviewers for helpful comments.
PY - 2004/5/28
Y1 - 2004/5/28
N2 - This paper presents a multiscale method that yields a stabilized finite element formulation for the advection-diffusion equation. The multiscale method arises from a decomposition of the scalar field into coarse (resolved) scale and fine (unresolved) scale. The resulting stabilized formulation possesses superior properties like that of the SUPG and the GLS methods. A significant feature of the present method is that the definition of the stabilization term appears naturally, and therefore the formulation is free of any user-designed or user-defined parameters. Another important ingredient is that since the method is residual based, it satisfies consistency ab initio. Based on the proposed formulation, a family of 2-D elements comprising 3 and 6 node triangles and 4 and 9 node quadrilaterals has been developed. Numerical results show the good performance of the method on uniform, skewed as well as composite meshes and confirm convergence at optimal rates.
AB - This paper presents a multiscale method that yields a stabilized finite element formulation for the advection-diffusion equation. The multiscale method arises from a decomposition of the scalar field into coarse (resolved) scale and fine (unresolved) scale. The resulting stabilized formulation possesses superior properties like that of the SUPG and the GLS methods. A significant feature of the present method is that the definition of the stabilization term appears naturally, and therefore the formulation is free of any user-designed or user-defined parameters. Another important ingredient is that since the method is residual based, it satisfies consistency ab initio. Based on the proposed formulation, a family of 2-D elements comprising 3 and 6 node triangles and 4 and 9 node quadrilaterals has been developed. Numerical results show the good performance of the method on uniform, skewed as well as composite meshes and confirm convergence at optimal rates.
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U2 - 10.1016/j.cma.2003.12.047
DO - 10.1016/j.cma.2003.12.047
M3 - Article
AN - SCOPUS:1842636700
SN - 0045-7825
VL - 193
SP - 1997
EP - 2018
JO - Computer Methods in Applied Mechanics and Engineering
JF - Computer Methods in Applied Mechanics and Engineering
IS - 21-22
ER -