LECTURE: | MWF 1100 - 1150 | BEXL 412 | CRN 39581 |
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Instructor: | R.E. Showalter | Kidder 286 | show@math.oregonstate.edu |

The minimization of quadratic functions over closed convex subsets has classical applications to boundary-value problems for elliptic partial differential equations, variational inequalities and optimal control problems, penalty or augmented Lagrangian methods and mixed formulations. We shall develop these ideas and applications to boundary-value problems and algorithms for their approximation. These topics will be placed in the more general context of convex analysis, saddle points and Lagrange multipliers, primal and dual problems in Hilbert space. These concepts will be illustrated with examples from mechanics (internal or boundary obstacles, friction), fluid flow (Stokes or Bingham flow) and diffusion (heat conduction, porous media flow).

The choice of Topics covered and Examples developed will depend in part on preferences of the class.

Special topics from linear analysis will be developed or described as needed. Contact instructor for questions about prerequisites or content, especially for general science or engineering students.

Accommodations for students with disabilities are determined and approved by Disability Access Services (DAS). If you, as a student, believe you are eligible for accommodations but have not obtained approval please contact DAS immediately at 541-737-4098 or at theirwebsite. DAS notifies students and faculty members of approved academic accommodations and coordinates implementation of those accommodations. While not required, students and faculty members are encouraged to discuss details of the implementation of individual accommodations.

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2. Preview, pp. 1 - 4 in

3. pp. 5 - 8 in

4.

5. Examples of BVPs.

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7.

8. Projection: pp. 13 - 15 in

9. minimization again!, pp. 169 - 172 in

10. derivative pp. 172 - 174. (01/30)

11. monotone, coercive pp. 174 - 177.

12. Examples: boundary constraints, pp. 178-180 in

13. Examples: interior constraints, pp. 15 - 18 in

14. Examples: continued; start reading Section II.2: Sobolev spaces in

15. Section II.3: Boundary Trace

16. Inf-sup condition, pp. 1-2 in

17. Equivalent conditions, p.3.

18. Mixed fornulation and Lagrange multiplier, pp, 3-5.

19. Saddle point & Lagrangian, pp, 6-7. (02/20)

20. p. 7-8.

21. p. 8-9.

22. No class. 02/27)

23. No class.

24. Neumann problem, pp. 9-11 in

25. Trace & Normal Trace, p. 12. (03/06)

26. Dirichlet-Neumann Problem, pp. 13-14.

27. Mechanics 101.

28. Stokes Equation, pp. 20-21 in

29. pp. 22-23.