Mathematics

Numerical Solution of Partial Differential Equations (L.6)

Module code: G5217
Level 6
15 credits in spring semester
Teaching method: Lecture
Assessment modes: Unseen examination, Coursework

You will learn how to develop computational methods for the approximation of PDEs and rigorously prove their accuracy. As part of a computational project, you will also implement these methods and illustrate that the computational results agree with the developed theoretical analysis.

Topics that will be covered include the variational formulation of boundary value problems, Sobolev spaces, abstract variational problems, the Lax-Milgram Lemma, the Galerkin method, the finite element method, elementary approximation theory, and error analysis.

Module learning outcomes

• Gain a basic understanding of the rationale and construction of finite element spaces;
• Demonstrate an elementary understanding of functional spaces and approximation theory;
• Demonstrate a knowledge of the basic ideas underlying discretization of partial differential equations using finite element methods;
• Analyse simple second order elliptic problems and derive error estimates for their numerical approximation