Journal
COMPUTATIONAL MECHANICS
Volume 38, Issue 4-5, Pages 323-333Publisher
SPRINGER
DOI: 10.1007/s00466-006-0036-y
Keywords
Darcy flow; mixed Galerkin methods; stabilization; projection; least-squares methods
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We consider finite element methods for the Darcy equations that are designed to work with standard, low order C-0 finite element spaces. Such spaces remain a popular choice in the engineering practice because they offer the convenience of simple and uniform data structures and reasonable accuracy. A consistently stabilized method [20] and a least-squares formulation [18] are compared with two new stabilized methods. The first one is an extension of a recently proposed polynomial pressure projection stabilization of the Stokes equations [5,13]. The second one is a weighted average of a mixed and a Galerkin principles for the Darcy problem, and can be viewed as a consistent version of the classical penalty stabilization for the Stokes equations [8]. Our main conclusion is that polynomial pressure projection stabilization is a viable stabilization choice for low order C-0 approximations of the Darcy problem.
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