Math 6630: Numerical Solutions of Partial Differential Equations:
Selected Numerical Methods
Instructor: Yekaterina Epshteyn
Lectures: TTh 3:40 PM - 5:00 pm, LCB 121
Office Hours (tentative, it may be some changes)
TBA
Office: LCB 337
E-mail: epshteyn@math.utah.edu
References
Claes Johnson, Numerical Solution of Partial Differential Equations by the Finite Element Method, Dover Publications
Stig Larsson and Vidar Thomee, Partial Differential Equations
with Numerical Methods, Texts in Applied Mathematics, Springer
Randall J. LeVeque, Finite Difference Methods for Ordinary and Partial Differential Equations: Steady-State and Time-Dependent Problems, SIAM
Randall J. LeVeque, Numerical Methods for Conservation Laws, Birkhauser
Jan Hesthaven and Tim Warburton, Nodal Discontinuous Galerkin Methods: Algorithms, Analysis, and Applications, Springer, 2008
John Strikwerda, Finite Difference Schemes and Partial Differential Equations, SIAM
Kendall Atkinson, An Introduction to Numerical
Analysis, Wiley
Victor S. Ryaben'kii and Semyon V. Tsynkov, A Theoretical Introduction
to Numerical Analysis, Chapman & Hall/CRC
Arieh Iserles, A First Course in the Numerical Analysis of
Differential Equations, Second Edition, Cambridge University Press
Dietrich Braess, Finite elements, Third Edition, Cambridge
The course
Math 6630 is the one semester of the graduate-level introductory course on the
numerical methods for partial differential equations (PDEs). Selected
topics on Finite Difference, Finite
Element, Finite Volume and Mesh Free Approximations Methods will be
discussed during the course. Accuracy, stability, and efficiency of the algorithms will be studied from
both a theoretical and computational standpoint. Applications to
problems from Biology (e.g., chemotaxis models), Fluid Dynamics (e.g.,
shallow water models), Materials Science (e.g., Fokker-Planck models), etc. will be discussed as well.
Homework
Homework will be assigned and collected, and will include theoretical analysis
and computational assignments. The computational part should be done using MATLAB, software produced by The MathWorks. The Matlab language provides extensive library of mathematical and scientific function calls entirely built-in. Matlab is available on Unix and Windows. The full set of manuals is on the web in html format. The "Getting Started" manual is a good
place to begin and is available in
Adobe
PDF format.
6630 Tentative Topics:
Topics will include: selected numerical methods and algorithms for elliptic
problems; parabolic problems; hyperbolic
problems; convection-diffusion problems. Applications.
ADA Statement
The Americans with Disabilities Act requires that reasonable accommodations be
provided for students with physical, sensory, cognitive, systemic, learning and psychiatric disabilities.
Please contact me at the beginning of the semester to discuss any such accommodations for the course.
Grading: Homework 70% and Final Paper Presentation (TBA) 30%
Homework due dates will be announced and posted