20 October 2021
10:00
to
12:00
The join button will be published on the right (Above the view all button) 30 minutes before the seminar starts (login required).
OxPDE Short Courses
Please note that the list below only shows forthcoming events, which may not include regular events that have not yet been entered for the forthcoming term. Please see the past events page for a list of all seminar series that the department has on offer.
Past events in this series27 October 2021
10:00
to
12:00
Kaibu Hu
Further Information:
Structure: 4 x 2 hr Lectures
Part 1 - 27th October
Part 2 - 3rd November
Part 3 - 10th November
Part 4 - 17th November
Abstract
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)
3 November 2021
10:00
to
12:00
Kaibu Hu
Further Information:
Structure: 4 x 2 hr Lectures
Part 1 - 27th October
Part 2 - 3rd November
Part 3 - 10th November
Part 4 - 17th November
Abstract
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)
10 November 2021
10:00
to
12:00
The join button will be published on the right (Above the view all button) 30 minutes before the seminar starts (login required).
10 November 2021
10:00
to
12:00
Kaibu Hu
Further Information:
Structure: 4 x 2 hr Lectures
Part 1 - 27th October
Part 2 - 3rd November
Part 3 - 10th November
Part 4 - 17th November
Abstract
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)
17 November 2021
10:00
to
12:00
Kaibu Hu
Further Information:
Structure: 4 x 2 hr Lectures
Part 1 - 27th October
Part 2 - 3rd November
Part 3 - 10th November
Part 4 - 17th November
Abstract
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)
