Francis Aznaran

BSc (Warwick), MASt (Cantab), DPhil (Oxon)

Status

Postdoctoral Research Associate

https://aznaran.com

+44 1865 615121

ORCID iD

https://orcid.org/0000-0001-9843-9852

Research groups

Numerical Analysis

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

Prizes, awards, and scholarships

Combined EPSRC/MathWorks Scholarship at the PDEs CDT, Oxford Mathematics Institute (2018–2022).

Research interests

The finite element method for the PDEs of elasticity and thermodynamics, encompassing:

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

Further details

ICIAM 2023 minisymposium: Finite element complexes for structure-preservation in continuum mechanics.

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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.

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Oxford FEM reading group.

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SIAM Annual Meeting 2022 minisymposium: Nonlinear Viscous Flow: Numerical Methods and Applications, MS30 Part I, MS57 Part II, MS85 Part III.

Major / recent publications

Finite element methods for multicomponent convection-diffusion, F. R. A. Aznaran, P. E. Farrell, C. W. Monroe, and A. J. Van-Brunt, submitted, Aug. 2022 (arXiv:2208.11949).
Transformations for Piola-mapped elements, F. R. A. Aznaran, P. E. Farrell, and R. C. Kirby, SMAI Journal of Computational Mathematics (to appear), 2023 (arXiv:2110.13224).

Teaching

Hilary '23: Tutor, Part C Finite Element Methods for PDEs.
Michaelmas '22: Tutor, Part B Functional Analysis I.
Hilary '22: Tutor, Part C Fixed Point Methods for Nonlinear PDEs.
Michaelmas '21: Tutor, MMSC Numerical Solution of PDEs.
Hilary '21: Tutor, Part B Functional Analysis II; TA, Part C Finite Element Methods for PDEs.
Michaelmas '20: TA, Part C Functional Analytic Methods for PDEs; TA, MMSC Numerical Solution of Differential Equations I.
Nov '20: Marker, Oxford MAT.
Hilary '20: TA, Part B Functional Analysis II.
Michaelmas '19 - Trinity '20: Tutor of Prelims Introductory Calculus, and marker of Collections, Oriel College.