# NCMW - Finite Element Methods for PDEs(2023)

## Speakers and Syllabus

**Syllabus:**

Name of the Speaker with affiliation |
No.of Lectures |
Detailed Syllabus |

Sheetal Dharmatti, Assistant Professor, School of Mathematics, IISER Thiruvananthapuram | 3 lectures of 1 and half hours each | Overview of Weak derivatives, Sobolev spaces and embeddings, Poincare inequality, Dual spaces, trace spaces. |

S. Kesavan, Professor, The Institute of Mathe- matical Sciences, Chennai | 4 lectures of 1 and half hours each | Some abstract variational problems (Stampac- chia, Lax Milgram, Babuska Brezzi), Examples of elliptic problems, Regularity of weak solu- tions. |

Neela Nataraj Profes- sor, Department of Mathe- matics, Indian Institute of Technology Bombay | 4 lectures of 1 and half hours each | Conforming, Mixed FEM, dGFEM for second order elliptic equations, Interpolation, and ap- proximation, Error estimates. |

Nagaiah Chamakuri, Assistant Professor, School of Mathematics, IISER Thiruvananthapuram | 4 lectures of 1 and half hours each | Discretization of Poisson’s problem. Aspects of efficient implementation: Mesh handling and data structure, Numerical integration, Sparse matrix storage, Local and global assembly of system matrices and load vectors, including vari- ous boundary conditions, and solving the assem- bled system. |

Asha K Dond, As- sistant Professor, School of Mathematics, IISER Thiruvananthapuram | 2 lectures of 1 and half hours each | Stokes Problem- Mixed FEM formulation, Error estimates. Aspects of efficient implementation. |

## Time Table

Time/Day |
11-09-2022 |
12-09-2022 |
13-09-2022 |
14-09-2022 |
15-09-2022 |
16-09-2022 |

09:00-10:30 | SD | SK | SK | NN | NN | NN |

10:30-11:00 | Tea | Tea | Tea | Tea | Tea | Tea |

11:00-12:30 | SK | SD | NC | NC | AD | AD |

12:30-14:00 | Lunch | Lunch | Lunch | Lunch | Lunch | Lunch |

14:00-15:30 | SD | SK | NC | NN | NC | NC |

15:30-16:00 | Tea | Tea | Tea | Tea | Tea | Tea |

16:00-17:00 | T(AK+NR) | T(NC+NR) | T(AD+AVS) | T(AD+RK) | T(NC+NR) |

** Note:** T(XYZ): Discussion class/Lab session by XYZ. Some aspects of implementation in MATLAB will be integrated in the lectures. Participants will be provided lab facilities outside of the lecture hours.

Full forms for the abbreviations of speakers and tutors:

• Speakers

– SD: Sheetal Dharmatti (Assistant Professor, School of Mathaematics, IISER Thiruvananthapuram)

– AD: Asha K Dond (Assistant Professor, School of Mathaematics, IISER Thiruvananthapuram)

– NC: Nagaiah Chamakuri (Assistant Professor, School of Mathaematics, IISER Thiruvananthapuram)

– SK: S. Kesavan (Professor, The Institute of Mathematical Sciences, Chennai)

– NN: Neela Nataraj (Professor, Department of Mathematics, IIT Bombay, Mumbai)

• Tutors

– RK: Rakesh Kumar (Postdoc, School of Mathaematics, IISER Thiruvananthapuram)

– NR: Nishant Ranwan (PhD, School of Mathaematics, IISER Thiruvananthapuram)

– AVS: Aswin V.S (Assistant Professor, Amrita Vishwa Vidyapeetham, Coimbatore)

• References

– S. Kesavan, Topics in Functional Analysis and Applications, New Age International Private Limited, 2015.

– E. Süli & David F. Mayers, An Introduction to Numerical Analysis, Cambridge University Press, 2003.

– S.C. Brenner & L.R. Scott, The Mathematical Theory of Finite Element Methods. Springer, 2nd edition, 2002.

– C. Johnson, Numerical Solution of Partial Differential Equations by the Finite Element Method. CUP, 1990.

– J.C. Strikwerda, Finite difference schemes and Partial differential equations, Wordsworth and Brooks, 1989.

– H. Elman, D. Silvester & A. Wathen, Finite Elements and Fast Iterative Solvers. Second edition, 2014.

– Sashikumaar Ganesan & Lutz Tobiska, Finite elements: Theory and Algorithms, Cambridge University Press, 2017.

– P.G. Ciarlet, The finite element method for elliptic problems, North-Holland, 1978.

– D. Di Pietro and A. Ern. Mathematical Aspects of Discontinuous Galerkin Methods. Mathématiques et Applications. Springer Berlin Heidelberg, 2011.