# Francis Aznaran

Society of Science Research Fellow in Applied and Computational Mathematics, University of Notre Dame.

**Research interests:**

- Piola transformation theory and implementation of finite element bases
- Elasticity complexes and the discretisation of elastic stress and strain
- Multicomponent fluid flows
- Fluid-structure interaction

**Preprints:**

*Finite element methods for multicomponent convection-diffusion*, Sept. 2022, arXiv:2208.11949 [bib, pdf]

**Publications:**

*Transformations for Piola-mapped elements*, SMAI Journal of Computational Mathematics, Vol. 8 (2022), pp. 399–437, DOI: 10.5802/smai-jcm.91 [bib, pdf]

**Brief CV:**

- 2023–present:
**Society of Science Research Fellow in Applied and Computational Mathematics and Statistics**, University of Notre Dame, Indiana. - 2022–23:
**EPSRC Postdoctoral Research Associate (independent)**, Mathematical Institute, University of Oxford. - Mar–Apr 2023:
**Visiting Scholar**, Department of Mathematics, Baylor University, Texas. - 2018–22:
**DPhil candidate in Numerical Analysis/OxPDE**(via the EPSRC CDT in PDEs), The Queen's College, University of Oxford. - Thesis:
*Discretisation of Hodge Laplacians in the elasticity complex*. - 2017–18:
**MASt Applied Mathematics (Part III)**, Corpus Christi College, University of Cambridge. - Essay:
*Highly oscillatory quadrature*. - 2014–17:
**BSc Mathematics**, University of Warwick.

**Awards:**

**Further information:**

- ICIAM 2023 minisymposium:
*Finite element complexes for structure-preservation in continuum mechanics*. - Summer project available:
*Nonlinear elasticity and Newton's method in infinite dimensions*, with Dr Charles Parker II, for 3^{rd}/4^{th}year undergraduates at Oxford. - Oxford FEM reading group is now organised by Charles Parker II; see here for texts covered Jan 2020 – Aug 2023.
- SIAM Annual Meeting 2022 minisymposium:
*Nonlinear viscous flow: Numerical methods and applications*. MS30 Part I, MS57 Part II, MS85 Part III.

**Contact:**

242 Hayes-Healy Center, Notre Dame, Indiana, 46556, USA