FOUNDATIONS OF FINITE ELEMENT METHODS

Beatrice Riviere

Fall 2023

    Meeting time and place: T Th 1:00pm-2:15pm, DH 1075
    Office Hours: by appointment (send email to: riviere at rice dot edu) DH 3019
    Course Objectives
    This course addresses the theory and implementation of finite element methods. Topics include weak solutions of partial differential equations, Sobolev spaces, approximation theory, convergence and reliability of the numerical methods. Continuous and discontinuous finite element methods are considered. The course number is CMOR 526.
    Course Outcomes
    Upon completion of the course, students have a good understanding of the theory of finite element methods, the approximation of Sobolev functions, the proof of well-posedness of finite element methods, as well as the convergence proof of continuous and discontinuous finite element methods.
    Grading
    Homeworks (70%) and paper review (30%).
  • Homework 1: due 9/26
  • Homework 2: due 10/17
  • Homework 3: due 11/16
    Paper Reviews
    Paper reviews will take place on November 28 and 30.
    Textbooks
    The Mathematical Theory of Finite Element Methods, by Suzanne C. Brenner and L. Ridgeway Scott, Publisher Springer.
    Homeworks
    In general, you may discuss homework problems with classmates, but you have to write your solution individually. Some homeworks may be pledged. Students are strongly encouraged to start their homeworks early.
    Additional reading
    Sobolev Spaces, by Robert A. Adams.
    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).
    Theory and Practice of Finite Elements by Alexandre Ern and Jean-Luc Guermond, Pubsliher Springer 2004.
    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 may 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%. Homeworks that are more than one week late will not be graded.
    Disability
    If you have a documented disability that may affect academic performance, you should make sure this documentation is on file with Disability Resource Center (Allen Center, Room 111 / adarice@rice.edu / x5841) to determine the accommodations you need, and meet with me to discuss your accommodation needs.
    Title IX
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