MATH 272:
NUMERICAL
METHODS
FOR
PDE
Instructor: Randolph E. Bank

The class meets MWF, 3:003:50, AP&M 2402.

Office hours are 4:005:00 Wednesday, AP&M 5771.

While the lectures will not be taken directly from any textbook, there
are a number of books that can be used as references.

Numerical Approximations of Partial Differential Equations,
by Alfio Quarteroni and Alberto Valli.
(Springer Series in Computational Mathematics,
Volume 23, ISBN 9783540852681)
Electronic Version.

PDEs with Numerical Methods,
by Stig Larsson and Vidar Thomee.
(Springer Texts in Applied Mathematics, Volume 45, ISBN 9783540017721,
hardcover, and 9783540887058, softcover)
Electronic Version.

The Mathematical Theory of Finite Element Methods
by Susanne C. Brenner and L. Ridgway Scott
(Springer Texts in Applied Mathematics, Volume 15, ISBN 9780387759340)
Electronic Version.
Math 272A  Fall Quarter 2018
Basic Discretization Methods

Two point Boundary Value Problem

Review some basic theory (existence, uniqueness, stability...)

Finite difference methods, basic error estimates

Finite element methods, basic error estimates

Elliptic Equations in Two and Three Space Dimensions

Finite difference methods, basic error estimates

Finite element methods, basic error estimates

Finite volume (box) methods, basic error estimates

Introduction to Computational Fluid Dynamics

ConvectionDiffusion Equations, upwinding, PetrovGalerkin methods

Stokes and NavierStokes Equations
Math 272B  Winter Quarter 2019
Basic Solution Methods

Iterative Methods for Sparse Systems of Equations

Classical Iterative Methods (Jacobi, GaussSeidel, SOR)

Conjugate Gradient, Biconjugate Gradient Methods

ILU and SSOR Preconditioners

Multigrid, Domain Decomposition and Hierarchical Basis Methods

Sparse Direct Methods

Nonlinear Equations

Newton's Method in the PDE Environment

Eigenvalue Problems
Math 272C  Spring Quarter 2019
Time Dependent Problems and Adaptive Methods

Basic Time Discretization Schemes

Introduction to Stiff ODE's

Method of lines discretization, basic error estimates

Spacetime finite element methods, moving mesh methods

Introduction to Adaptive Methods

A Posteriori error estimates

Adaptive mesh refinement algorithms

Adaptive mesh moving algorithms

hp adaptive finite element methods
