Seminar series
Date
Wed, 03 Nov 2021
Time
10:00 - 12:00
Location
L3
Speaker
Kaibu Hu
Organisation
Oxford University

Many PDE models encode fundamental physical, geometric and topological structures. These structures may be lost in discretisations, and preserving them on the discrete level is crucial for the stability and efficiency of numerical methods. The finite element exterior calculus (FEEC) is a framework for constructing and analysing structure-preserving numerical methods for PDEs with ideas from topology, homological algebra and the Hodge theory. 

 

In this seminar, we present the theory and applications of FEEC. This includes analytic results (Hodge decomposition, regular potentials, compactness etc.), Hodge-Laplacian problems and their structure-preserving finite element discretisation, and applications in electromagnetism, fluid and solid mechanics. Knowledge on geometry and topology is not required as prerequisites.

 

References:

 

1. Arnold, D.N.: Finite Element Exterior Calculus. SIAM (2018) 

2. Arnold, D.N., Falk, R.S., Winther, R.: Finite element exterior calculus, homological techniques, and applications. Acta Numerica 15, 1 (2006) 

3. Arnold, D.N., Falk, R.S., Winther, R.: Finite element exterior calculus: from Hodge theory to numerical stability. Bulletin of the American Mathematical Society 47(2), 281–354 (2010) 

4. Arnold, D.N., Hu, K.: Complexes from complexes. Foundations of Computational Mathematics (2021)

Further Information

Structure: 4 x 2 hr Lectures

Part 1 - 27th October

Part 2 - 3rd November

Part 3 - 10th November

Part 4 - 17th November

Please contact us with feedback and comments about this page. Last updated on 03 Apr 2022 01:32.