n-Dimensional Variational Problems

  • Susanne C. Brenner
  • L. Ridgway Scott
Part of the Texts in Applied Mathematics book series (TAM, volume 15)


We now give several examples of higher-dimensional variational problems that use the theory developed in previous chapters. The basic notation is provided by the Sobolev spaces developed in Chapter 1. We combine the existence theory of Chapter 2 together with the approximation theory of Chapters 3 and 4 to provide a complete theory for the discretization process. Several examples will be fully developed in the text, and several others are found in the exercises. Throughout this chapter, we assume that the domain Ω is bounded.


Variational Problem Variational Formulation Adjoint Problem Piecewise Polynomial Natural Boundary Condition 
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Copyright information

© Springer Science+Business Media New York 2002

Authors and Affiliations

  • Susanne C. Brenner
    • 1
  • L. Ridgway Scott
    • 2
  1. 1.Department of MathematicsUniversity of South CarolinaColumbiaUSA
  2. 2.University of ChicagoChicagoUSA

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