Postdoctoral Research Fellow

We are inviting applications for a Postdoctoral Research Fellow Position, as part on the EPSRC project Advanced Numerical Methods for Mean Field Games, Grant EP/Y008758/1.

Deadline for applications: 09 May 2024.

Link to details and instructions on how to apply.

Funded PhD Position in Numerical analysis

Applications are invited for a PhD studentship in Numerical Analysis in the Department of Mathematics at University College London. The research theme is the development and analysis of numerical methods for mean field games, under the supervision of Dr Iain Smears, Associate Professor in Applied Mathematics. The funding is for 4 years, and includes tuition fee at Home (UK) rate, an annual stipend, and an allowance for research costs.

Further details, including instructions on how to apply, are provided on this page:
www.ucl.ac.uk/maths/home/vacancies/phd-studentship-mathematical-sciences.

Current Students

Mr Yohance Osborne, PhD student

Former postdocs

Dr Ellya Kawecki, EPSRC Doctoral Prize Fellowship, 2019—2021

Publications

23. Near and full quasi-optimality of finite element approximations of stationary second-order mean field games, Yohance A. P. Osborne & IS, submitted, 2024.

arXiv

22. Finite element approximation of time-dependent mean field games with non-differentiable Hamiltonians, Yohance A. P. Osborne & IS, submitted, 2023.

arXiv

21. Analysis and numerical approximation of stationary second-order mean field game partial differential inclusions, Yohance A. P. Osborne & IS, SIAM Journal on Numerical Analysis, 2024. doi:10.1137/22M1519274.

SINUM arXiv

20. Convergence of adaptive discontinuous Galerkin and C0-interior penalty finite element methods for Hamilton–Jacobi–Bellman and Isaacs equations, E. L. Kawecki & IS, Foundations of Computational Mathematics, 2021. doi:10.1007/s10208-021-09493-0

FOCM arXiv

19. Unified analysis of discontinuous Galerkin and C0-interior penalty finite element methods for Hamilton–Jacobi–Bellman and Isaacs equations, E. L. Kawecki & IS, ESAIM Math. Model. Numer. Anal., 2021. doi:10.1051/m2an/2020081

ESAIM M2AN arXiv

18. Equivalence of local-and global-best approximations, a simple stable local commuting projector, and optimal hp approximation estimates in H(div), Alexandre Ern, Thirupathi Gudi, IS & M. Vohralik, IMA Journal of Numerical Analysis, 2021. doi:10.1093/imanum/draa103

IMANUM arXiv HAL

17. Simple and robust equilibrated flux a posteriori estimates for singularly perturbed reaction-diffusion problems, IS & M. Vohralik, ESAIM Math. Model. Numer. Anal., 2020, doi:10.1051/m2an/2020034.

ESAIM M2AN arXiv HAL

16. Time-parallel iterative solvers for parabolic evolution equations, M. Neumüller & IS, SIAM Journal on Scientific Computing, 2019, doi:10.1137/18M1172466.

SISC arXiv

15. An adaptive hp-refinement strategy with computable guaranteed bound on the error reduction factor, P. Daniel, A. Ern, IS & M. Vohralik, Computers and Mathematics with Applications, 2018, doi:10.1016/j.camwa.2018.05.034.

CAMWA arXiv HAL

14. Equilibrated flux a posteriori error estimates in L²(H¹)-norms for high-order discretizations of parabolic problems, A. Ern, IS & M. Vohralik, IMA Journal of Numerical Analysis, 2018, doi:10.1093/imanum/dry035.

IMANUM arXiv HAL

13. On the notion of boundary conditions in comparison principles for viscosity solutions, M. Jensen & IS, in Hamilton–Jacobi– Bellman Equations, Numerical Methods and Applications in Optimal Control, Radon Series on Computational and Applied Mathematics, 2018.

PDF arXiv HAL

12. Nonoverlapping domain decomposition preconditioners for discontinuous Galerkin approximations of Hamilton–Jacobi–Bellman equations, IS, Journal of Scientific Computing, volume 74, issue 1, pages 145–174, 2018 (published online 2017).

JSC PDF © Springer arXiv HAL

11. Guaranteed, locally space-time efficient, and polynomial-degree robust a posteriori error estimates for high-order discretizations of parabolic problems, A. Ern, IS & M. Vohralik, SIAM Journal on Numerical Analysis, volume 55, issue 6, pages 2811-2834, 2017.

SINUM pdf © SIAM arXiv HAL

10. Discrete p-robust H(div)-liftings and a posteriori estimates for elliptic problems with H⁻¹ source terms, A. Ern, IS & M. Vohralik, Calcolo, volume 54, issue 3, pages 1009-1025, 2017.

Calcolo arXiv HAL

9. Robust and efficient preconditioners for the discontinuous Galerkin time-stepping method, IS, IMA Journal of Numerical Analysis, volume 37, issue 4, pages 1961-1985, 2017.

IMANUM arXiv HAL

8. Stable Discontinuous Galerkin FEM without penalty parameters, L. John, M. Neilan & IS, Numerical Mathematics and Advanced Applications 2015, pages 165-173, Springer, 2016.

Springer arXiv HAL

7. A note on optimal spectral bounds for nonoverlapping domain decomposition preconditioners for hp-version discontinuous Galerkin methods, P. F. Antonietti, P. Houston & IS, International Journal of Numerical Analysis and Modeling, volume 13, issue 4, pages 513–524, 2016.

Int. J. Numer. Anal. Model.

6. Discontinuous Galerkin finite element methods for time-dependent Hamilton–Jacobi–Bellman equations with Cordes coefficients, IS & E. Süli, Numerische Mathematik, volume 133, issue 1, pages 141-176, 2016.

Numer. Math. arXiv

5. Discontinuous Galerkin finite element approximation of Hamilton–Jacobi–Bellman equations with Cordes coefficients, IS, DPhil Thesis, University of Oxford, 2015.

Oxford Thesis Repository

4. Discontinuous Galerkin finite element approximation of Hamilton–Jacobi–Bellman equations with Cordes coefficients, IS and E. Süli, SIAM Journal on Numerical Analysis, volume 52, issue 2, pages 993–1016, 2014.

SINUM pdf © SIAM

3. Discontinuous Galerkin finite element approximation of nondivergence form elliptic equations with Cordes coefficients, IS and E. Süli, SIAM Journal on Numerical Analysis, volume 51, issue 4, pages 2088–2106, 2013.

SINUM pdf © SIAM

2. Finite element methods with artificial diffusion for Hamilton–Jacobi–Bellman equations, M. Jensen and IS, Numerical Mathematics and Advanced Applications 2011, pages 267-274, Springer, 2013.

Springer arXiv

1. On the convergence of finite element methods for Hamilton–Jacobi–Bellman equations, M. Jensen and IS, SIAM Journal on Numerical Analysis, volume 51, issue 1, pages 137–162, 2013.

SINUM pdf © SIAM