MAT-INF4310 - Vår 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. Påskedag 
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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