The Stokes Equations

  • Pavel B. BochevEmail author
  • Max D. GunzburgerEmail author
Part of the Applied Mathematical Sciences book series (AMS, volume 166)

The key juncture in this process is the identification of the energy balances for the first-order systems. The Agmon–Douglis–Nirenberg (ADN) and the vector-operator settings, already encountered in Chapters 5 and 6, are used here as well. For CLSPs defined in the ADN setting, transition to DLSPs relies on the abstract least-squares theory for ADN systems formulated in Chapter 4. Accordingly, error analysis of the resulting LSFEMs is simply a matter of specializing that theory to the first-order Stokes systems. LSFEMs in the ADN setting for the Stokes system are considered in Sections 7.2–7.6. Formulation and analysis of LSFEMs in the vector-operator setting is somewhat more involved because this setting results in non-conforming methods similar to those encountered in Section 6.3.3. However, the vector-operator setting is well worth the effort because it allows us to formulate, for some sets of non-standard boundary conditions (but, unfortunately, not for the velocity boundary condition), locally conservative LSFEMs for the Stokes equations, a feat that is very difficult, if not impossible, to accomplish in the ADN setting. LSFEMs in the vector-operator setting for the Stokes system are considered in Section 7.7.


Stokes Equation Normal Velocity Element Space Stokes System Minimization Space 
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Copyright information

© Springer-Verlag New York 2009

Authors and Affiliations

  1. 1.Sandia National LaboratoriesApplied Mathematics and Applications MS 1320AlbuquerqueUSA
  2. 2.Florida State UniversityDepartment of Scientific ComputingTallahasseeUSA

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