250079 VO Topics in Finite Elements (2022S)

This course focuses on advanced topics in finite element methods for the approximation of partial differential equations. The first part of the course will be dedicated to the introduction to discontinuous Galerkin finite element methods for an elliptic model problem. In the second part of the course, students will be introduced to the Reduced Basis Method. The focus will be the presentation of the Greedy Algorithm, the Proper Orthogonal Decomposition, some a posteriori error estimators and the Empirical Interpolation Method. The example of application will be the heat equation. Further topics may depend on students interests and may include discontinuous Galerkin finite element methods for an advection-reaction equation or applications of the Reduced Basis Method to the Stokes problem.