Numerical Methods for Partial Differential Equations

What it is about

You will learn numerical solution methods for partial differential equations, in particular finite element methods for multi-dimensional elliptic boundary value problems. You will also learn error estimates, adaptive mesh refinement, fast solvers and an introduction to numerical methods for time-dependent problems. In the end you will be able to understand the methods, apply them and use the associated software.

What you will be able to do

• Apply numerical solution techniques for partial differential equations
• Understand a priori- and a posteriori error analysis
• Perform adaptive mesh refinement
• Use efficient solvers for discretized systems
• Know the basics of numerical methods for evolution equations
• Develop programming skills and use appropriate software

What the module consists of

• VorlesungConveying theoretical content, examples and discussion
• Übung/PraktikumAccompanying problems, programming exercises and deepening of the lecture material
• SelbststudiumWorking on problem sheets and literature study for consolidation

Teaching method

• Lectures with demonstration examplesfor introduction and explanation of the methods
• Discussion with studentsfor deepening and critical engagement with the topics
• Exercise sheets with solutionsto check understanding and train practical skills
• Guided and later independent practice sessionsto increasingly promote independent work and group work