MTH5323 · Advanced numerical analysis of partial differential equations

Overview

This unit introduces the numerical approximation of partial differential equations, with a focus on both the mathematical foundations and the practical usages of these notions. Topics covered include weak formulations of partial differential equations (PDEs) in primal and mixed form; abstract saddle-point problems; conforming and non-conforming finite element methods; finite volume methods; mixed finite element methods; stability and convergence analysis; implementation of computational schemes.

Areas of study: Master of Mathematics

Offerings

The Handbook publishes no offerings for this unit.

Assessment

The Handbook lists an examination for this unit.

Assessment details may change. Please refer to the assessment information in Moodle closer to the start of the teaching period.

Requisites

Learning outcomes

1. Describe and rigorously analyse sophisticated numerical methods for PDEs;
2. Implement numerical methods for standard models including diffusion and linear elasticity;
3. Demonstrate understanding of the mathematical properties of advanced numerical methods, and use this understanding to select appropriate method for each specific problem;
4. Communicate and critically discuss the outcome of numerical methods for PDEs.

Workload

• Two 1.5 -hour seminars; • One 1-hour applied class (in weeks 2-12) and • Eight hours of independent study per week.

Student experience, not official rules. Nothing here changes what the Handbook says.