Instructor: Bojan Popov
Office: Blocker 608J
Email: popov"at"math.tamu.edu
Phone: 845-1989
Office Hours: TR 10:20-11:20, or by appointment
Textbook: R.J. LeVeque, Numerical Methods for Conservation Laws, 2nd ed., Birkauser 1992.
Prerequisites: Math 612 or Math 609-610, or instructor's approval
Outline: This is a topic course for graduate students who are interested in nonlinear first order PDEs and their applications. I plan to cover: (i) The basic existence-uniqueness theory for scalar conservation laws; (ii) Consider special equations/systems of interest for various application and solve the Riemann problems for such systems; (iii) The stability for viscous perturbations and simple numerical methods. There will be no required book for the class but LeVeque's book above is a good reference. I will also use lecture notes, papers and the following references:
1. Lawrence C. Evans, Partial Differential Equations (Graduate Studies in Mathematics, V. 19) GSM/19
2. H. Holden, and N.H. Risebro, Front Tracking for Hyperbolic Conservation Laws,Springer Verlag, New York 2002.
3. E. Tadmor, Approximate solutions of nonlinear conservation laws, in "Advanced Numerical Approximation of Nonlinear Hyperbolic Equations", Lecture notes in Mathematics 1697, 1997 C.I.M.E. course in Cetraro, Italy, June 1997 (A.~Quarteroni ed.) Springer Verlag 1998, 1-149.
Grading system: Due to the wide range of applications, this course should be of interests to students in aerospace and atmospherics sciences, and also nuclear engineering, etc. Therefore, formal, in class theoretical exams are not appropriate for this class. I will give a midterm and a final exam assignments.
Midterm (exam/project): 50% Final (exam/project): 50%
Make-Up Policy: Make-ups for exams will only be given with documented University-approved excuses (see University Regulations). Consistent with University Student Rules, students are required to notify an instructor by the end of the second working day after missing an exam. Otherwise, they forfeit their rights to a make-up.
Scholastic Dishonesty: Students may work together and discuss the homework problems with each other. Copying work done by others is an act of scholastic dishonesty and will be prosecuted to the full extent allowed by University policy. For more information on university policies regarding scholastic dishonesty, see University Student Rules .
Copyright Policy: All printed hand-outs and web materials are protected by US Copyright Laws. No multiple copies can be made without written permission by the instructor.
Students with Disabilities: The Americans with Disabilities Act (ADA) is a federal anti-discrimination statute that provides comprehensive civil rights protection for persons with disabilities. Among other things, this legislation requires that all students with disabilities be guaranteed a learning environment that provides for reasonable accommodation of their disabilities. If you believe you have a disability requiring an accommodation, please contact Disability Services, in Cain Hall, Room B118, or call 845-1637.
Lectures 1-4 Introduction to Conservation Laws, mathematical principles, weak solutions, scalar Riemann problems, Rankine-Hugoniot condition. A good source is LeVeque (pages 1-35) and the notes.
Lectures 5-8 A crash course in Godunov-type schemes: Holden-Risebro (pages 63-77), my notes and the paper