Course: Math 272A: Numerical Partial Differential Equations I
Class meet time and location: TuTh 5pm-6:20pm, APM 2402
Office hours: Wednesday 2-3pm and Thursday 4-5pm, APM 5755
Credit Hours: 4
Prerequisite: Graduate standing or consent of instructor.
Catalog Description: Survey of discretization techniques for elliptic partial differential equations, including finite difference and finite element methods. Lax-Milgram Theorem and LBB stability. A priori error estimates. Mixed methods. Convection-diffusion equations. Systems of elliptic PDEs. Prerequisites: graduate standing or consent of instructor.
Suggested books:
- Numerical PDEs:
Numerical Approximation of Partial Differential Equations. A. Quarteroni and A. Valli, Springer-Verlag, 1994.
The Mathematical Theory of Finite Element Methods, Third Edition. S.C. Brenner and L.R. Scott, Springer-Verlag, 2008.
Lecture Notes on Numerical Analysis of Partial Differential Equations. Douglas N. Arnold, 2018.
- PDE theory:
Elliptic Partial Differential Equations of Second Order, Second Edition. David Gilbarg and Neil S. Trudinger, Springer, 2001.
Partial Differential Equations, Second Edition. Lawrence C. Evans, American Mathematical Soc., 2010.
- Functional analysis & approximation theory:
Functional Analysis, Sobolev Spaces and Partial Differential Equations. Haim Brezis, Springer, 2011.
Green's Functions and Boundary Value Problems. I. Stakgold and M. Holst, John Wiley & Sons, 2011.
Lecture: Lectures will be held in person at APM 2402. Lectures will also be recorded and made available on Podcast. Attending the lecture (or reviewing the recording) is a fundamental part of the course; you are responsible for material presented in the lecture whether or not it is discussed in the textbook. You should expect questions on the exams that will test your understanding of concepts discussed in the lecture.
Homework: All homework is due on Fridays 11:59pm (Pacific Time) online. Submission is through Gradescope.
Late homework will not be accepted. Two lowest scores will be dropped in the end.
Each homework may contain both analytical and programming problems. You are allowed to use any preferred programming languages. Code used in class and provided for homework solutions will be in
Matlab. Please read the homework assignments guidelines below.
- Programming problem requirements:
1. Describe the method/algorithm used to solve the problem.
2. Discuss the numerical experiments conducted(specify input/output and the parameters used).
3. Report the key observations of the numerical experiments. Provide some analysis (performance, results) and offer a conclusion
4. Use tables/graphics to summarize the data/output from experiments to support the analysis and conclusion.
5. Attach the computer program written for the project as supplementary materials.
Note:
a. Please avoid turning in pages of computer programs output without explanation.
b. Please provide captions to tables, legends for pictures/plots. - Collaboration policy:
1. It is okay to discuss the problems with others, but you must write your own solutions.
2. For the programming problems, it is okay to work on the development and debugging with others, but you must do your own runs, make your own plots, etc.
3. If you worked together with someone on a homework assignment, you must write down who you worked with.
Exam: There will be a take-home final exam.
Grading:
Your grade in the course will be based on these three metrics: homework (50%) + take-home final (30%) + class participation (20%) .
Academic Integrity: Academic integrity is highly valued at UCSD and academic dishonesty is considered a serious offense. Students involved in an academic integrity violation will face an administrative sanction which may include suspension or, in very serious cases, expulsion from the university. Your integrity has great value: Cultivate and protect your academic integrity. For more about academic integrity and its value, visit the UCSD Academic Integrity Website.