Math 6630: Numerical Solutions of Partial Differential Equations:
Finite Element Methods
Instructor: Yekaterina Epshteyn
Lectures: MW 11:50 am - 1:10 pm, ST 214
Office Hours
TBA
Office: LCB 337
E-mail: epshteyn@math.utah.edu
Textbook and References
Main Textbook:
Claes Johnson, Numerical Solution of Partial Differential Equations by the Finite Element Method, Dover Publications
References:
Stig Larsson and Vidar Thomee, Partial Differential Equations
with Numerical Methods, Texts in Applied Mathematics, Springer
Dietrich Braess, Finite elements, Third Edition, Cambridge
Alexandre Ern and Jean-Luc Guermond, Theory and Practice of
Finite Elements, Series: Applied Mathematical Sciences, Vol. 159,
Springer, 2004
Jan Hesthaven and Tim Warburton, Nodal Discontinuous Galerkin
Methods: Algorithms, Analysis, and Applications,
Springer, 2008
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
Randall J. LeVeque, Finite Difference Methods for Ordinary and Partial Differential Equations: Steady-State and Time-Dependent Problems, SIAM
John Strikwerda, Finite Difference Schemes and Partial Differential Equations, SIAM
David Gottlieb and Steven Orszag, Numerical Analysis of
Spectral Methods: Theory and Applications, SIAM
Eitan Tadmor, A Review of Numerical Methods for Nonlinear
Partial Differential Equations, pdf
The course
Math 6630 is the one semester of the graduate-level introductory course on the
numerical methods for partial differential equations (PDEs). Finite
Element Methods (FEM) for linear and nonlinear problems will be the main emphasis of the course. If time
will permit introduction to other numerical methods for PDEs will be discussed as well. Accuracy, stability, and efficiency of the algorithms will be studied from
both theoretical and computational standpoint. Applications to problems
from Biology, Fluid Dynamics, Materials Science, etc. will be
discussed as well.
Prerequisite
The course will be self-contained. Introductory knowledge of Numerical
Analysis and Partial Differential Equations is recommended.
Homework
We will have about 4 homework assignments during the semester. 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: introduction to finite element
methods (FEM) for elliptic problems; FEM for parabolic problems; hyperbolic
problems; applications.
Safety Statement
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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