Partial Differential Equations

This schedule is designed to give you an overview of the material to be covered and is tentative in nature. This is a living document and will be updated throughout the semester.

The entries in the column References point to a number of standard references in the field. See my webpage on recommended literature for the complete citations.

Class | Date | Main Topic | References |

1 | Tu 01/31 | Overview of prototype problems for the semester | Evans (Ch. 1) |

2 | Th 02/02 | Theory of elliptic partial differential equations | Evans (Sec. 2.2) |

3 | Tu 02/07 | Theory of parabolic partial differential equations | Evans (Sec. 2.3) |

4 | Th 02/09 | The finite difference method for elliptic problems | Braess (Ch. I) |

5 | Tu 02/14 | Linear solvers and Matlab programming | |

6 | Th 02/16 | Theory of the finite difference method for elliptic problems | Braess (Ch. I) |

7 | Tu 02/21 | Theory of the finite difference method for elliptic problems | Braess (Ch. I) |

8 | Th 02/23 | Test 1 (the finite difference method)
| |

9 | Tu 02/28 | Introduction to the FEM for elliptic problems | |

10 | Th 03/02 | The weak form of elliptic PDEs | |

11 | Tu 03/07 | Weak derivatives and Sobolev spaces and their norms | Braess (Sec. II.1) |

12 | Th 03/09 | General theory of elliptic bilinear forms | Braess (Sec. II.2) |

13 | Tu 03/14 | Céa's lemma and Galerkin orthogonality | Braess (Sec. II.4) |

We 03/15
| 12:00-01:00 CIRC Software Workshop on FEMLAB
| in Room ENG 122
| |

14 | Th 03/16 | More on weak formulation and introduction to FEMLAB | |

Tu 03/21 | Spring Break | ||

Tu 03/21 | Spring Break | ||

15 | Tu 03/28 | Standard finite element spaces and their properties | Braess (Sec. II.5) |

16 | Th 03/30 | Implementation details of finite element methods | |

Fr 03/31
| The Finite Element Circus at UMBC | in Room BIOL 120
| |

Sa 04/01
| The Finite Element Circus at UMBC | in Room BIOL 120
| |

17 | Tu 04/04 | Approximation theory for finite element spaces | Braess (Sec. II.6) |

18 | Th 04/06 | Convergence analysis for the FEM for elliptic problems | Braess (Sec. II.7) |

19 | Tu 04/11 | Introduction to FEMLAB's scripting language | |

20 | Th 04/13 | Test 2 (the finite element method)
| |

21 | Tu 04/18 | The method of lines for parabolic problems (FEM and FD) | |

22 | Th 04/20 | The finite element method for parabolic problems | Thomée (Ch. 1) |

23 | Tu 04/25 | Theory of the finite element method for parabolic problems | Thomée (Ch. 1) |

24 | Th 04/27 | Theory of hyperbolic partial differential equations | Strikwerda (1.1-1.2) |

25 | Tu 05/02 | Finite differences for the scalar transport equation | Strikwerda (1.3-1.4) |

26 | Th 05/04 | Theory for FD for the scalar transport equation | Strikwerda (1.5-1.6) |

27 | Tu 05/09 | Numerical methods for stiff systems of ODEs | Shampine & Reichelt |

28 | Th 05/11 | Numerical methods for stiff systems of ODEs | Shampine & Reichelt |

29 | Tu 05/16 | Review and discussion | |

Th 05/18
| 01:00-03:00 Project Presentations
| Note date and time!
| |

Copyright © 1999-2006 by Matthias K. Gobbert. All Rights Reserved.

This page version 1.6, May 2006.