A stabilized mixed finite element method for Darcy flow based on a multiscale decomposition of the solution

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• 作者：K.B. Nakshatrala ; D.Z. Turner ; K.D. Hjelmstad and A. Masud
• 关键词：Darcy flow ; Mixed methods ; Multiscale formulation ; Stabilized finite elements
• 刊名：Computer Methods in Applied Mechanics and Engineering
• 出版年：2006
• 出版时间：1 July 2006
• 年：2006
• 卷：195
• 期：33-36
• 页码：4036-4049
• 全文大小：627 K

文摘

Recently Masud and Hughes proposed a stabilized mixed finite element formulation for Darcy flow. An interesting feature of this formulation is that there are no mesh-dependent parameters. In the present work we provide a derivation of this formulation based on a multiscale decomposition of the solution. We also extend the work of Masud and Hughes to three-dimensional problems and show the convergence rates for various three-dimensional finite elements. We also show that this formulation passes three-dimensional constant-flow patch tests for distorted element geometries (i.e., elements with non-constant Jacobian). Robustness of this formulation is illustrated by performing numerical simulations on complex geometries.