MAT-INF4310 - V?r 2004

Teaching plan

DateTeacherPlaceTopicLecture notes / comments
26.01.2004Snorre Christiansen (SC)? B81? Introduction and Lax-Milgram theorem? Overview of the contents of the course. Started on chapter 6. Uniformly elliptic operators. Lax-Milgram Theorem. (§6.1.1 to §6.2.1) ?
30.01.2004? ? Applications of Lax Milgram to elliptic PDE? Continuity and boundedness. §6.2.2 (Theorem 2 and 3 p. 300, 301). Problem 1 p. 345. §D.1 to §D.3. ?
02.02.2004? ? Functional Analysis? Reviewed material from Folland's book and properties of H^{-1} according to Notes I.?
06.02.2004? ? Fredholm alternative? §D.4 and §D.5 (Theorem 4 and 5 p. 640, 641) and §6.2.3 (Theorem 4 p. 303)?
09.02.2004? ? Eigenvalues? Corrected exercises on Notes II. §D.5 (Theorem 6 p. 643) and §6.2.3 (Theorem 5 p. 305)?
13.02.2004? ? Eigenvalues (symmetric case)? Theorem 7 p. 645 and Theorem 1 p. 335?
16.02.2003? ? Local H^2 regularity? Theorem 1 p. 309?
20.02.2003? ? Higher order local regularity? Theorem 2 p. 314 and Theorem 3 p. 277. Exercise III.2.1.?
23.02.2004? ? No teaching? Abroad. Read all exercises and do as many as possible.?
27.02.2003? ? No teaching? Abroad?
01.03.2004? ? H^2 regularity up to the boundary? Theorem 3 p. 316 and Theorem 4 p. 317?
05.03.2004? ? Comments? Coordinate transformations and partitions of unity. Problem 2. p. 345. Exercise IV.1.1.?
08.03.2004? ? Higher order regularity up to the boundary? Theorem 5 p. 323?
12.03.2004? ? Finite elements? Galerkin method. Minimization property for symmetric case. Cea's lemma. §II.2.4 (p. 53-56) in Braess book.?
15.03.2004? ? Some finite element spaces? (2D case) Finite element meshes with triangular elements. Space of continuous piecewise polynomials. (§II.2.5, p. 60-66)?
19.03.2003? ? Interpolation estimates for FE spaces? Bramble-Hilbert lemma. (similar to §II.2.6 p. 76-79, Theorem 6.4 for m=1)?
22.03.2003? ? Converge rate for FE on convex domain? Theorem 6.6 p. 80 and Theorem 7.2 p. 89 without proofs and Theorem 7.3 p. 90 (Combine Cea & Bramble-Hilbert & Regularity). Exercise VII.1.1?
26.03.2003? ? L2 estimates for FE method? Aubin Nitsche trick p. 91. Exercises VII.1.2, VII.1.3 and III.2.2.?
29.03.2004? ? Overview? I'll sum up how far we have come.?
02.04.2004? ? More finite elements? Inverse inequalities (Theorem 6.8 p. 83 for t=1 and m=0) and stability of the L2 projector (Corollary 7.8 p. 94; NB : H^1_0 setting, not H^1). Exercise II.6.13 p. 87 in Braess.?
05.04.2004? ? Easter? ?
09.04.2004? ? Easter? Langfredag?
12.04.2004? ? Easter? 2. P?skedag?
16.04.2004? ? Evolution equations, ? Introduction, Appendix E.5 and §5.9.2 p. 285 in Evans.?
19.04.2004? ? Spaces involving time? §5.9.2 Theorem 3 p. 287 and Theorem 4 p. 288 (without proof). Problem 3 p. 345.?
23.04.2004? ? Heat equation? Remarks on last time. Linear ODE with L^1(End(E)) coefficients. Heat equation. Weak solutions (§7.1.1).?
26.04.2004? ? PDE workshop? Attend the CMA workshop on PDE. More info here : http://www.cma.uio.no/?
30.04.2004? ? Existence and uniqueness.? Energy estimates. Convergence of Galerkin solutions to weak solutions. Uniqueness. (§7.1.2). ?
03.05.2003? ? Exercises? Problem 4 p. 425 in Evans. Essentially IX.1.1?
07.05.2004? ? Exercises? Problem 3 p. 425 in Evans. Exercise VIII.2.1 and VIII.2.2?
10.05.2004? ? No teaching? Abroad?
14.05.2004? ? No teaching? Abroad?
17.05.2004? ? No teaching? 17. Mai!?
21.05.2004? ? Exercises (weak convergence)? Problem 1 p. 487 in Evans. IX.2.1.?
24.05.2004? ? Exercises? IX.4.1, IX.4.2 and VIII.1.1.?
28.05.2004? ? Exercises? Exercise VI.2.1. Some material from Thomee's book (SCM Vol. 25). ?
31.05.2004? ? No teaching ? 2. Pinsedag?
Publisert 27. okt. 2003 16:30 - Sist endret 26. mai 2004 11:34
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