
LECTURE: 
Duncan Hall 3076, 1011am Wednesdays 


INSTRUCTOR: 
Jesse Chan (jesse.chan@rice.edu)
Duncan Hall 3023, (713) 3486113 


OFFICE HOURS: 
Wednesdays 1112am or by appointment.



PREREQUISITE: 
Background in numerical analysis, linear algebra, and MATLAB programming.



GRADING: 
Projects and presentations. 


SYLLABUS: 
pdf 


TEXTS: 
Nodal Discontinuous Galerkin Methods: Theory and Application by Jan Hesthaven and Tim Warburton.



RECOMMENDED TEXTS 
Implementing spectral methods for partial differential equations: Algorithms for scientists and engineers by David Kopriva


Mathematical aspects of discontinuous Galerkin methods by Daniele Di Pietro and Alexandre Ern


Discontinuous Galerkin Methods for Solving Elliptic and Parabolic Equations: Theory and Implementation by Beatrice Riviere.


MATLAB Guide
by Desmond J. Higham and Nicholas J. Higham, 2nd ed., SIAM, 2005




Lecture schedule: 
Lecture 13 (4/18): Final project presentations.


Lecture 12 (4/11): variable coefficient advection problems, curved meshes.


Lecture 11 (4/4): curvilinear meshes, stability of the skewsymmetric matrix formulation. Code for curved meshes curved meshes.


Lecture 10 (3/28): curvilinear meshes, cont.


Lecture 9 (3/14): curvilinear meshes. Wave code for heterogeneous media.


Lecture 8 (3/7): Cancelled (instructor out of town). 

Lecture 7 (2/28): Twodimensional acoustics, boundary conditions, second order formulations. Variable coefficients. 

Lecture 6 (2/21): Twodimensional acoustic wave equation. wave2d_demo.m 

Lecture 5 (2/14): Twodimensional problems. 2D DG codes 

Lecture 4 (2/7): Convergence, symmetric hyperbolic systems, the acoustic wave equation. Advection convergence code and acoustic wave equation demo. 

Lecture 3 (1/31): Energy stability, upwind/dissipative/penalty numerical fluxes, periodic boundary conditions. Modified advection code: advec1D_periodic.m 

Lecture 2 (1/24): Nodal bases, 1D advection code (for download here). To run code, unzip and "cd" into directory and run advec1D.m. 

Lecture cancelled (1/17): bad weather. 

Lecture 1 (1/10): Lecture 1: class overview, timedependent hyperbolic PDEs, high order DG methods for 1D advection. 





Homeworks: 
Homework 1 (due Feb 21). 

Homework 2 (TBA). 


