Prof. Volker John from Weierstrass Institute (WIAS) and Freie University Berlin is visiting the Department of Mathematics, IIT Roorkee during January 21-31, 2020. During his stay, he will be delivering a talk on "Algebraic Finite Element Stabilizations for Convection-Diffusion Equations" in the Computer Lab of the department at 4:30 pm on January 24, 2020.
Lecture Series on "Numerical Methods for Convection-Dominated Equations"
Speaker: Prof. Volker John (Weierstrass Institute & Freie University Berlin)
Date: 27- 30 January 2020
Time: 05:00 P.M.
Venue: Computer Lab, Mathematics
Abstract: This lecture series provides an introduction into numerical methods for solving scalar convection-diffusion equations. Such equations model conservation laws, like energy conservation via an equation for the temperature. In many practical cases, convection dominates diffusion and then the solution of these equations possess so-called layers, which are very thin structures that cannot be resolved on affordable grids. Standard discretizations cannot cope with this situation and the use of so-called stabilized discretizations is necessary.
In the lecture series, various stabilized discretizations in the framework of finite difference, finite element, and finite volume methods will be discussed. Some fundamental proofs, or at least sketches of proofs, concerning the discrete maximum principle, i.e., that the solution is physically consistent, and concerning the convergence of the methods will be given. Numerical examples illustrate the behavior of the methods.
About the Speaker:
The Mathematical Colloquium of the Department of Mathematics is organising a "Research Scholars' Day" on 17 January 2020. There will be 11 talks and 3 poster presentations by PhD students on the topics of various interest.