# Francis Aznaran

Postdoctoral research associate (independent), Numerical Analysis group, Oxford Mathematical Institute.

**Research interests:**

- Piola transformation theory and implementation of finite element bases
- Elasticity complexes and the discretisation of elastic stress and strain
- Multicomponent fluid flows
- Multigrid, preconditioning, and fast solvers

**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:**

- 2022–present:
**EPSRC Postdoctoral Research Associate (independent)**, Mathematical Institute, University of Oxford. - Mar–Apr 2023:
**Visiting Scholar**, Department of Mathematics, Baylor University, Texas. - 2018–2022:
**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, for 3^{rd}/4^{th}year undergraduates at Oxford. - Oxford FEM reading group.
- SIAM Annual Meeting 2022 minisymposium:
*Nonlinear viscous flow: Numerical methods and applications*. MS30 Part I, MS57 Part II, MS85 Part III.

**Contact:**

Mathematical Institute, University of Oxford, Andrew Wiles Building, Radcliffe Observatory Quarter, Woodstock Road, Oxford, OX2 6GG, UK