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B. Riviere


CAAM 452 NUMERICAL SOLUTIONS OF PARTIAL DIFFERENTIAL EQUATIONS

Spring 2012

    Meeting time and place:T Th 1:00pm-2:15pm, KCK 101
    Office Hours:Th 10am-11am and by appointment (send email to: riviere at rice dot edu) DH 3022
    Content
    This course covers various numerical methods for solving partial differential equations. We will mostly study the theory and the implementation of finite difference methods and finite element methods. Elliptic and parabolic problems are considered. We will also consider other methods such as finite volume methods, mixed methods, discontinuous Galerkin methods, meshless methods.
    Objectives
    Upon completion of the course, students have a good understanding of both finite difference and finite element methods. They will have developped codes for solving elliptic and parabolic equations in 1D and 2D using those two methods.
    Grades
    Homeworks (90%) and midterm (10%).
    Midterm
    The midterm is a pledged exam and access to lecture notes only is allowed.
    Textbooks
    Finite Difference Methods for Ordinary and Partial Differential Equations: Steady-State and Time-Dependent Problems by Randall J. LeVeque, SIAM, 2007.
    Understanding and Implementing the Finite Element Method by Mark S. Gockenbach, SIAM, 2006.
    Homeworks
    In general, you may discuss homework problems with classmates, but you have to write your solution individually. Some homeworks are pledged. Homeworks will contain both theoretical and computational problems. Students are strongly encouraged to start their homeworks early.
    Homework1: due on January 26. Uses fdstencil.m
    Homework2: due on February 14. Uses poisson.m
    Additional reading
    Numerical Analysis of Partial Differential Equations by Charles Hall and Thomas Porsching, Prentice Hall (1990).
    Sobolev Spaces, by Robert A. Adams.
    The Mathematical Theory of Finite Element Methods, by Suzanne C. Brenner and L. Ridgeway Scott, Publisher Springer.
    The Finite Element Method for Elliptic Problems, by Philippe G. Ciarlet.
    Handbook of Numerical Analysis: Volume II, Finite Element Methods by Philippe G. Ciarlet and Jacques-Louis Lions, North Holland, NY (1991).
    Discontinuous Galerkin Methods for Solving Elliptic and Parabolic Equations: Theory and Implementation, by Beatrice Riviere, Publisher SIAM.
    Nodal Discontinuous Galerkin Methods: Algorithms, Analysis, and Applications, by Jan S. Hesthaven and Tim Warburton, Publisher Springer.
    Class web site
    Students are responsible for viewing the class web site regularly as material will be added to the site throughout the semester.
    Late policy
    Homeworks are to be given during class on the due date. If the homework is turned in after the class is over, it is considered late. Late homeworks will incur penalties in increments of 10%.
    Disability
    Any student with a documented disability requiring accomodations in this course is encouraged to contact me after class or during office hours. Additionally, students also need to contact Disability Support Services in the Ley Student Center.