Introduction to the finite element method and its application to singularly perturbed problems

Lecturer: Prof. Dr. Roman Drebotiy (University of Lviv, Ukraine)

Contents

Based on the advection-diffusion-reaction model, we introduce the finite element method and explore its fundamental properties. We discuss key aspects of the variational nature behind the method and derive basic error estimates. Two different approaches are considered for addressing so-called singularly perturbed problems, which are characterized by an imbalance between processes. Using the derived estimates, we construct a simple mesh adaptation scheme to overcome the singular perturbations of the problem. Additionally, we develop a finite element stabilization technique based on well-known regularization methods and discuss the differences between the two schemes.

Certificate

No credit points are granted for this lecture, since the total amount of hours is too low. A certificate of attendance can be issued.

Required Knowledge

Basic knowlege in: analysis, linear algebra, ordinary differential equations, numerical mathematics.

Target audience

B.Sc. Mathematik, B.Sc. Mathematik mit Informatik, M.Sc. Mathematik und M.Sc. Biomathematik

Schedule

This lecture is a block course of 8 hours in the week November 11-15, 2024.

11.11., 4-6 pm, SR 2

12.11., 2-4 pm, SR 2

13.11., 2-4 pm, SR 5

15.11., 2-4 pm, SR 5

Literature

R. Verfürth: Adaptive Finite Element Methods. Lecture Notes.