Textbook: Numerical Analysis of Partial Differential Equations, Charles Hall and Thomas Porsching, Prentice Hall, New Jersey 1990.
Course Info: This course presents the theory and methodology of the numerical solutions of partial differential equations. It covers both the finite difference and the finite element methods, has both a practical and an analytical nature, and contains basic theoretical results at a level that is understandable to beginning graduate students in engineering and in the sciences. Topics covered include, among others: prototypal problems, hyperbolic systems, parabolic diffusion equation, Lax-Richtmyer theory, Sobolev spaces, elliptic boundary value problems and so on. It will cover chapters 1-7 of the textbook. Prerequisites include advances calculus, linear algebra, and differential equations.
Homework: There will be some theoretical assignments and some practical assignments which involve some computer programming.
Computing. As a computing language we will use Matlab.
Submission of the work in other languages is allowed, but no support will
be provided. Please consult the Web page of the class for pointers
to additional material including a Matlab primer.
Other references:
James W. Thomas
Numerical Partial Differential Equations: Finite difference methods, Springer 1995.
Stig Larsson, Vidar Thomee
Partial Differential Equations with Numerical Methods, Springer 2003.
Vidar Thomee
Galerkin finite element methods for parabolic problems, Springer 2006.
Haim Brezis
Functional Analysis, Sobolev Spaces and Partial Differential Equations, Springer 2011.
Willem Hundsdorfer and Jan G. Verwer
Numerical Solution of Time-Dependent Advection-Diffusion-Reaction Equations, Springer 2003.
Alfio Quarteroni, Alberto Valli
Numerical Approximation of Partial Differential Equations, Springer 1994.
Lawrence C. Evans
Partial Differential Equations, American Mathematical Society, American Mathematical Society 1998.
Viorel Barbu
Nonlinear Differential Equations of Monotone Types in Banach Spaces, Springer 2010.
Viorel Barbu
Nonlinear Semigroups and Differential Equations in Banach Spaces, Springer 1976.
Viorel Barbu
Partial Differential Equations and Boundary Value Problems, Springer 1998.
Giovanni Paolo Galdi
An Introduction to the Mathematical Theory of the Navier-Stokes Equations. Steady-State Problems, Springer 2011.
Roger Temam
Navier-Stokes equations. Theory and numerical analysis, AMS Chelsea Publishing 1984.
Vivette Girault, Pierre-Arnaud Raviart
Finite Element Methods for Navier-Stokes Equations. Theory and Algorithms, Springer 1986.
Jeffery M. Cooper
Introduction to Partial Differential Equations with MATLAB, Birkhäuser 2000.
The author's collection of mfiles are available at:
http://www.math.umd.edu/~jcooper/PDEbook/mcodes.html.