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

In this module, you will learn about:

• 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
• error analysis.

Module learning outcomes

• Gain fundamental 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