CAAM 552 · Foundations of finite element methods
Spring 2017 · Rice University
PROBLEM SETS //
PIAZZA //
PAPER PRESENTATIONS //
 CLASS: 
2:30PM  3:45PM Tuesday/Thursday Abercrombie Lab A121 


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


OFFICE HOURS: 
Wednesday 12pm or by appointment.



GRADING: 
70% problem sets, 30% paper reviews 


TEXTS: 
The Mathematical Theory of Finite Element Methods by Susanne Brenner and L. Ridgeway Scott
Discontinuous Galerkin Methods for Solving Elliptic and Parabolic Equations: Theory and Implementation by Beatrice Riviere
An analysis of the finite element method by Gilbert Strang and George Fix
Nodal Discontinuous Galerkin Methods: Algorithms, Analysis, and Applications by Jan Hesthaven and Tim Warburton
Mathematical Aspects of Discontinuous Galerkin Methods by Daniele Di Pietro and Alexandre Ern //



SYLLABUS: 
pdf 


LECTURES: 
Lecture 1: Introduction, onedimensional formulations (Brenner and Scott, Chapter 1)
Lecture 2: weak derivatives, Sobolev spaces (Brenner and Scott, Chapter 2)
Lecture 3: trace theorems in Sobolev spaces (Brenner and Scott, Chapter 2)
Lecture 4: symmetric variational formulations, the LaxMilgram theorem (Brenner and Scott, Chapter 2)
Lecture 5: nonsymmetric variational formulations, generalized LaxMilgram theorem (Brenner and Scott, Chapter 2)
Lecture 6: coercive variational formulations, Poisson's equation (Brenner and Scott, Chapter 5)
Lecture 7: Poisson's equation, pure Neumann boundaries, meshes (Brenner and Scott, Chapter 5, Chapter 3)
Lecture 8: Finite elements: definition and interpolants (Brenner and Scott, Chapter 3)
Lecture 9: Interpolation estimates: approximation results for averaged Taylor polynomials (Brenner and Scott, Chapter 4)
Lecture 10: Interpolation estimates (Brenner and Scott, Chapter 4)
Lecture 11: Finite element error estimates (Brenner and Scott, Chapter 5)
Lecture 12: Finite element error estimates for parabolic problems (Strang and Fix)
Lecture 13: Finite element error estimates for the 2nd order wave equation (Strang and Fix)
Lecture 14: Nonconforming methods (Brenner and Scott)
Lecture 15: Nonconforming methods: CrouzeixRaviart, DG methods for Poisson's equation (Brenner and Scott)
Lecture 16: NIPDG methods for Poisson: coercivity and continuity (Brenner and Scott)
Lecture 17: SIPDG methods for Poisson: coercivity and continuity (Brenner and Scott)
Lecture 18: DG methods for advectionreaction: central fluxes (Di Pietro and Ern)
Lecture 19: Central flux DG for advectionreaction: coercivity, continuity, and convergence (Di Pietro and Ern)
Lecture 20: Upwind flux DG for advectionreaction: coercivity, continuity(Di Pietro and Ern)
Lecture 21: Upwind flux DG for advectionreaction: convergence (Di Pietro and Ern)
Lecture 22: Second order DG methods: SIPG in mixed formulation
Lecture 23: Second order DG methods: LDG and upwinding, variable contrast diffusivity
Lecture 24: Timedependent hyperbolic systems: semidiscrete error analysis
Lecture 25: Timedependent hyperbolic systems: discrete error analysis



Any student with a disability requiring accommodation in this course is encouraged
to contact the instructor during the first week of class, and also to contact
Disability Support Services in the Ley Student Center.
