Francis Aznaran
BSc (Warwick), MASt (Cantab), DPhil (Oxon)
Status
Postdoctoral Research Associate
Research groups
Address
Mathematical Institute
University of Oxford
Andrew Wiles Building
Radcliffe Observatory Quarter
Woodstock Road
Oxford
OX2 6GG
University of Oxford
Andrew Wiles Building
Radcliffe Observatory Quarter
Woodstock Road
Oxford
OX2 6GG
Major / recent publications
- Finite element methods for multicomponent convection-diffusion, Aznaran, F. R. A., Farrell, P. E., Monroe, C. W., and Van-Brunt, A. J., submitted, Sept. 2022 (arXiv:2208.11949).
- Transformations for Piola-mapped elements, Aznaran, F. R. A, Kirby, R. C., and Farrell, P. E. SMAI Journal of Computational Mathematics, Vol. 8 (2022), pp. 399–437, DOI: 10.5802/smai-jcm.91
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 3rd/4th year undergraduates at Oxford.
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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.
Prizes, awards, and scholarships
- Combined EPSRC/MathWorks Scholarship at the PDEs CDT, Oxford Mathematics Institute (2018–2022).
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.