Bio

Associate Professor in Applied Mathematics, University College London

Starting Research Position, INRIA Paris, 2015-2017

DPhil in Mathematics, University of Oxford, 2015

Interests

Numerical analysis and mathematical analysis of partial differential equations

Hamilton—Jacobi—Bellman equations, Mean Field Games

Fully nonlinear partial differential equations

A posteriori error analysis & adaptivity

Awards and Major Grants

EPSRC New Investigator Award, Grant EP/Y008758/1, starting July 2024 (3 year duration)

Appointment to Fellow of the Higher Education Academy (FHEA), 2020

17th IMA Leslie Fox 1st Prize, 2015

SIAM Student Paper Prize, 2014

Current Students and Postdocs

Dr Harry Wells, Postdoc, 2024—present

Former PhD students and Postdocs

Dr Yohance Osborne, UCL PhD 2020—2024

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

Publications

25. A posteriori error bounds for finite element approximations of steady-state mean field games, Yohance A. P. Osborne, IS & Harry Wells, submitted, 2025.
arXiv version
24. Regularization of stationary second-order mean field game partial differential inclusions, Yohance A. P. Osborne & IS, submitted, 2024.
arXiv version
23. Near and full quasi-optimality of finite element approximations of stationary second-order mean field games, Yohance A. P. Osborne & IS, Mathematics of Computation, 2025.
Journal version arXiv version
22. Finite element approximation of time-dependent mean field games with nondifferentiable Hamiltonians, Yohance A. P. Osborne & IS, Numerische Mathematik, 2024.
Journal version arXiv version
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.
Journal version Erratum arXiv version
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
Journal version arXiv version
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
Journal version arXiv version
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
Journal version arXiv version HAL version
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.
Journal version arXiv version HAL version
16. Time-parallel iterative solvers for parabolic evolution equations, M. Neumüller & IS, SIAM Journal on Scientific Computing, 2019, doi:10.1137/18M1172466.
Journal version arXiv version
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.
Journal version arXiv version HAL version
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.
Journal version arXiv version HAL version
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.
Journal version arXiv version HAL version
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).
Journal version arXiv version HAL version
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.
Journal version arXiv version HAL version
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.
Journal version arXiv version HAL version
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.
Journal version arXiv version HAL version
8. Stable Discontinuous Galerkin FEM without penalty parameters, L. John, M. Neilan & IS, Numerical Mathematics and Advanced Applications 2015, pages 165-173, Springer, 2016.
Journal version arXiv version HAL version
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.
Journal version
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.
Journal version arXiv version
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.
Journal version
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.
Journal version
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.
Journal version arXiv version
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.
Journal version arXiv version
PDF files of papers are shared with the permission of the copyright holders.