# Francis Aznaran

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:**

- Aznaran, F. R. A., Hu, K., and Parker II, C.,
*Uniformly hp-stable elements for the elasticity complex*, arXiv:2409.17414 (2024) [pdf, bib] - Aznaran, F. R. A., Bukač, M., Muha, B., and Salgado, A. J.,
*Analysis and finite element approximation of a diffuse interface approach to the Stokes–Biot coupling*, arXiv:2407.05949 (2024) [pdf, bib]

**Publications:**

- Aznaran, F. R. A., Farrell, P. E., Monroe, C. W., and Van-Brunt, A. J.,
*Finite element methods for multicomponent convection-diffusion*, IMA Journal of Numerical Analysis (2024), pp. 1–35, DOI: 10.1093/imanum/drae001 [pdf, bib] - Aznaran, F. R. A., Farrell, P. E., Kirby, R. C.,
*Transformations for Piola-mapped elements*, SMAI Journal of Computational Mathematics, Vol. 8 (2022), pp. 399–437, DOI: 10.5802/smai-jcm.91 [pdf, bib]

**Forthcoming talks:**

- 25
^{th}–26^{th}Apr 2025: Finite Element Circus, Oakland University (MI). - 21
^{st}–22^{nd}Feb 2025: Finite Element Rodeo, Louisiana State University.

**Brief CV:**

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

**Awards:**

- 1
^{st}prize, Postdoc Lightning Talk Competition, University of Notre Dame College of Science:*Numerical modelling of fluid and solid mechanics*(19^{th}Sept 2024). - Combined EPSRC/MathWorks Scholarship at the PDEs CDT, Oxford Mathematical Institute (2018–22).

**Further information:**

- Riverbend Community Math Center, South Bend, IN.
- Northern Indiana Regional Science and Engineering Fair.
- 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.
- ICIAM 2023 minisymposium:
*Finite element complexes for structure-preservation in continuum mechanics*. - SIAM Annual Meeting 2022 minisymposium:
*Nonlinear viscous flow: Numerical methods and applications*. MS30 Part I, MS57 Part II, MS85 Part III.

**Contact:**

203F Crowley Hall, Notre Dame, Indiana, 46556, USA