Advanced Numerical Methods: Discretizations 1000-1S25FEM
Although numerical methods have been an actively developing field for many years, there remains a significant amount of work to be done. In particular, when it comes to partial differential equations, using standard approaches can quickly face numerous barriers, both practical and theoretical.
Our goal will be to introduce participants to selected, currently developed and researched methods of discretizing such equations. We will start with classical literature on the finite element method and then progress to advanced topics: discontinuous Galerkin methods, CutFEM, hp-methods, approximations by neural networks, and so on. Our aim is to touch real research problems in this field
Type of course
Prerequisites (description)
Course coordinators
Learning outcomes
- Has knowledge of selected methods for discretizing partial differential equations.
- Is able to analyze the properties of the learned discretization methods based on literature.
- Is familiar with current research trends in this field.
- Is able to prepare and deliver presentations of varying length and level of generality.
Assessment criteria
Delivery of presentations, active participation and engagement.
Bibliography
- A.Quarteroni, A.Valli, Numerical Approximation of Partial Differential Equations, Springer 1994
- D.A. Di Pietro, A. Ern, Mathematical Aspects of Discontinuous Galerkin Methods, Springer 2012
and research/survey papers presented during the course of the seminar.
Additional information
Information on level of this course, year of study and semester when the course unit is delivered, types and amount of class hours - can be found in course structure diagrams of apropriate study programmes. This course is related to the following study programmes:
Additional information (registration calendar, class conductors, localization and schedules of classes), might be available in the USOSweb system: