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 (tentative, it may be some changes)

TBA, or by appointment
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.

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.

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