TMA4212 Numerical solution of differential equations by difference methods - Spring 2024

NTNU course description.

An oral exam on August 15 (and 16 if needed), 2024, room 1148, SB2 (Espen's office).
(I confirm that exam will oral).

• To get a time slot for the exam:
  
  
  • Email lecturer (Espen) as soon as possible and no later than August 5.
    
    
• The schedule and place for the exam:
  
  
  • Emailed to you on August 12.
  • The time slots may change (it will for many of you), but not the day.

• To keep your time slot:
  
  
  • Confirm that you will attend at the time slot you received August 12 …
  • … by email no later than August 13.

The exam will be a standard oral exam, where you answer questions for about 40 min. Paper and black/whiteboard will be available.

PS: Since I will not answer emails during my vacation, it is safest to contact me before July 5.

Messages

Date	Title	Message
16.05	Grading	… of final exams is completed. The results will appear in Studentweb soon. The grading document is available in Blackboard. \\
07.05	Exam 2024	Problems and Solutions Solutions for Problem updated 16.05. \\
18.04	Last lecture	Tuesday April 23. Exam problems. I will be away, Nanna will replace me.
	Office hours	Tuesday 30.04.: 14:15-16:00 in F6. Questions and answer session Friday 03.05.: 13:15-15:00 in EL1. Questions and answer session
	Project 2	Grades can be found in Ovsys, scale used to transform points to letters under "Exercises and projects". If you want to discuss, complain, or believe something is missed in the project evaluation, contact Nanna. Deadline: Friday April 26 at 16:00 After that the final project grades will be uploaded in Inspera.
	Last exercise class	Tuesday April 23. See below for question and answer sessions before the exam.
	Exam/curriculum	Read carefully the 'Course info' in the menu.
	Reference group	Last meeting today, see short summary in 'Reference group' in the menu.
12.04	Next week	Week 16. Tuesday: Last lecture on iterative methods. Thursday: Exam problems in lecture.
	Last lecture	Tuesday April 23. Exam problems. I will be away, Nanna will replace me.
	Reference group	meeting Thursday next week. I am very interested in feedback on the whole course and in particular the projects (e.g. work load, relevance, timing, collisions with other classes etc.).
	Final curriculum	Now available, see 'Course info' in the menu. Note the parts that differ from the note of Brynjulf Owren and the table showing you where to find these parts in my notes from the lectures.
	The exam	Updated info under 'Course info' in the menu.
08.04	Exercise 5	has been posted.
	Exercise class 09.04	There will not be any assistants in the room, instead come by Nanna's office (sentralbygg 2 room 1154) to ask questions.
04.04	Error in estimate from 19.03	The estimate should not have an exponent 2, correct: \[\inf_{v_h\in X^1_h}\|u-v_h\|_{H^1}\leq Ch \|u_{xx}\|_{L^2}.\]
03.04	Project supervision Wedensday	Nanna will be in room S21, and Ulrik will be on Zoom, link under "Exercises and projects"
19.03	Lectures	Thursday 21.03.: Supervision Project 2. Tuesday 02.04.: No lecture (Tuesday after Easter).
	Project 2	Check schedule carefully, see 'Exercises and Projects' in the menu. You know everything needed to solve the project after today's lecture if you assume (as you can!) that for \(u\in H^2\), \[\inf_{v_h\in X^1_h}\|u-v_h\|_{H^1}\leq Ch^2 \|u_{xx}\|_{L^2}.\] (Wrong, see message 04.04). Combining this estimate with Cea's lemma, give you the error estimate. Error in the text have been corrected, and you can now find an overview of project guidance.
05.03	Project 1	I (Nanna) have posted points and some feedback in Ovsys. Please note: - I have mainly tried to point out the main areas of improvement to explain why you (may) not have gotten a full score, so read them with that in mind; many good parts have not been mentioned. - If you believe I have overlooked something, have questions, or want to discuss your result, contact me. Either in the exercise classes or send an email, and we will find a suitable time. ( I am away in week 10).
	Project 2	… posted under "exercises and projects". Supervision times will come later.
	Reference group 2	Tuesday March 5, see 'Reference group' in the menu for a short summary.
04.03	No exercise class…	… on March 5 (Espen still has office hour).
	Office hour…	… this week on Thursday: 14:30-15:00 in my office (1148 SB2).
	FEM jupyter notebook	Available under 'Plan of the lectures', relevant from week 10.
26.02	Exercise class week 9	No attendence (understandable), so Nanna has gone back to her office (SB2 1154). Come by here if you planned on arriving the exercise class after I left.
26.02	Reference group	Meeting next week. Contact the group if you have feedback on the Project 1 or the course in general.
	Homework	Read yourselves: Von Neumann stability for Lax-Wendroff, the Leap frog method, systems of hyperbolic PDEs - BO section 7.
	Exercise 4	Available under 'Exercises and Projects'.
15.02	Project 1	Two small errors have been corrected in the project description, see under 'Exercises and Projects'.
	Exercise 3	Approvals can be found in ovsys.
13.02	Project 1	Deadline: 25.02. Schedule for supervision: Starting today(!) - see menu under 'Exercises and Projects'. Read carefully all instructions (report, submission, notebook etc.) given in the menu under 'Exercises and Projects'. Graded, counts for 20% of final grade.
05.02	Project 1	Published on exercise page. Deadline 25.02.
	Jupyter notebook 3	Posted under week 6 under 'Plan of lectures' in the menu.
02.02	Exercise 2	Solution to exercise 2 published.
01.02.	Reference group	First meeting Thursday 01.02. See 'Reference group' in the menu for a short summary. Lecture speed: Falling behind sometimes? Let me know and I will take a short break for you to catch up. Questions during class? Do not hesitate to ask. It does not have to be super thought through question (stupid is ok), others may also wonder. Just ask
	Exercise 3	Compulsory: Must be approved to access the exam. Deadline 11.02. Recommendation: Use the jupyter notebooks of the course as a basis of your own code! Modify only what you have to (or want to). This is ok, just mention in the report that you do so (details are not needed). Only groups can submit this exercise and later projects. If you do not have a group yet, contact Nanna as soon as possible. Times for supervision and all other info under 'Exercises and pojects' in the menu - check it carefully.
29.01.	Reference group	First meeting: Thursday 01.02. If you have feedback on the course, contact them (or me directly), see email addresses in 'reference group' in the menu. We will also discuss the deadline for project 1.
	Read yourselves:	a) The \(\theta\)-method (BO sec. 4.2.5) and stability of this method (BO p. 55-56) b) Read BO sec 5.3 on Domain of dependence. c) Discretization of B.C. (BO sec. 4.4 - similar to 1d Poisson!) OBS: You should be able to do simple convergence proofs.
24.01.	Reference group	Anja, Eva, Marius, and Per agreed to join the reference group. Thank you very much!
	Questions?	Need help? Want to discuss something? Use the weekly exercise classes, office hours, and/or contact me during lectures. See below for more detailed info.
	Exercise classes	Tuesdays 14-16, Hovedbygningen 326. Use them for help with exercises and programming/implementation in general.
	Jupyter notebook 2	Posted under week 4 under 'Plan of lectures' in the menu. Exercise 2 is built up around this notebook.
	Exercise 2	Available now, supervision week 4. Useful for later exercises and projects. The programming part can be solved by modifying appropriately the Jupyter notebook for week 4.
	Exercise 1	Solution published. Notification to Nanna of errors much appreciated.
	Homework	Download, test and check jupyter notebook 2.
16.01.	Today's lecture	Today's discussion deviate somewhat from BO, see the notes under 'Plan of lectures' in the menu. I have corrected a sign error at the end of the lecture.
11.01.	Slides	Slides will be posted weekly under 'Plan of Lectures' in the menu.
	My lecture notes	Since I sometimes deviate from the note of BO in my lectures, I will make an exception in this course and post my handwritten lecture notes weekly under 'Plan of Lectures' in the menu. Postings will always happen after the lectures have been given, when the notes have been corrected. Also note that there is bound to be some mistakes in the notes, so please let me know if you find any. If we find enough time, we will make a tex-ed version of the most important deviations: The discussion on error analysis using the discrete max principle.
	Exercise 1	Available now, supervision week 3. Problem 4 is useful for later exercises and projects, especially the programming part. The programming part can be solved by modifying appropriately the Jupyter notebook for week 2 and 3.
	Jupyter notebook 1.	See Week 2 under 'Plan of lectures' in the menu.
	Homework	Download, test and check jupyter notebook 1. Read BO section 2 (mostly known from before).
02.01.	First lecture	Tuesday January 9, 12:15-14:00.
	Exercise classes	Here you get help to solve exercises and projects. Programming and theory. Tuesdays 14-16, see more info below. No exercise class in week 2.
	Office hours	Questions about the course? Come and talk to me in class (breaks) or in the office hours. Tuesdays 14:30-15:00, in my office - room 1148 SB2. No office hour in week 2.
	Jupyter notebooks	Will be used to illustrate different methods in the course, and help you solve the exercises. How to run them? Take a look at 'Course Software Info' under 'Course info' in the menu.
	Exercises and projects	There will be a number of exercises and 2 projects in this course. These will focus on implementation (coding) and testing of numerical methods. There will also be theoretical problems. Mandatory: Exercise 3 and one out of two projects! 40% of the final grade: The 2 projects each count for 20% of the final grade. Groups: Exercise 3 and the projects are submitted by groups of up to 3 students. Check the info and schedule carefully, see 'Exercises and projects' in the menu.
	Exercise/Project groups	Send an email to Nanna with the 3 members (with email addresses) of your group. If you don't have a group, send an email, and you will be assigned to a group.
	No recordings in 2024	The lectures will not be recorded this semester, and previous recordings will not be available. The reason is very low attendance of the lectures Spring 2022 (recordings) compared to the good attendance Spring 2023 (no recordings). We want students on campus because we belive that most of you learn and socialise better here than at home. (It is also more fun to lecture when more students show up ). Exceptions can be made for "studenter med krav på tilrettelegging."

• Espen R. Jakobsen (espen [dot] jakobsen [at] ntnu [dot] no)
• Office hours (tentative): Tuesday 14:30 - 15:00, in my office, room 1148 SB2.

• Nanna Berre (nanna [dot] berre [at] ntnu [dot] no)
• Office hours: In the exercise class.

• Ulrik Unneberg (ulrikmu [at] stud [dot] ntnu [dot] no)

• Tuesday 12:15-14:00, EL1
• Thursday 12:15-14:00, EL1

• Tuesday 14:15-16:00, Hovedbygningen 326. Exception week 6: Realfagbygget D1-185