Mathematics

Numerical Solution of Partial Differential Equations (L.6)

Module code: G5217
Level 6
15 credits in spring semester
Teaching method: Lecture
Assessment modes: Coursework, Computer based exam

Topics covered include: variational formulation of boundary value problems; function spaces; abstract variational problems; Lax-Milgram Theorem; Galerkin method; finite element method; examples of finite elements; 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