A multiscale/stabilized finite element method for the advection-diffusion equation
A multiscale/stabilized finite element method for the advection-diffusion equation
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DOI：
10.1016/j.cma.2003.12.047
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发表时间：
2004-01-01
影响因子：
7.2
通讯作者：
Khurram, RA
中科院分区：
文献类型：
--
作者：
Masud, A;Khurram, RA
本文提出了一种多尺度方法，产生一个稳定的有限元列式的对流扩散方程。多尺度方法是将标量场分解为粗尺度（已分辨）和细尺度（未分辨）。所得稳定制剂具有与SUPG和GLS方法类似的上级性质。本方法的一个显著特征是稳定化项的定义自然出现，因此该公式不含任何用户设计或用户定义的参数。另一个重要的成分是，由于该方法是基于残差的，它满足从头算的一致性。基于所提出的公式，一族2-D单元，包括3和6节点三角形和4和9节点四边形已被开发。数值结果表明，该方法在均匀网格、斜网格和复合网格上都有良好的性能，并以最优速度收敛。(C)2004 Elsevier B. V.保留所有权利。
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 ingredients 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. (C) 2004 Elsevier B.V. All rights reserved.