Publications

Journal articles

Fully nonlinear second-order mean field games with nondifferentiable Hamiltonians, Thomas Sales & IS, submitted, 2025.

arXiv version

Rates of convergence of finite element approximations of second-order mean field games with nondifferentiable Hamiltonians, Yohance A. P. Osborne & IS, Mathematics of Computation, 2026. doi:10.1090/mcom/4189

Journal version arXiv version

On the efficiency of a posteriori error estimators for parabolic partial differential equations in the energy norm, IS, SMAI Journal of Computational Mathematics, volume 12, pages 27-42, 2026. doi:10.5802/jcm.142

Journal version arXiv version

A posteriori error bounds for finite element approximations of steady-state mean field games, Yohance A. P. Osborne, IS & Harry Wells, IMA Journal of Numerical Analysis, 2025. doi:10.1093/imanum/draf107

Journal version arXiv version

Regularization of stationary second-order mean field game partial differential inclusions, Yohance A. P. Osborne & IS, SIAM Journal on Mathematical Analysis, volume 57(5), pages 5189-5215, 2025. doi:10.1137/24M1686401.

Journal version arXiv version

Near and full quasi-optimality of finite element approximations of stationary second-order mean field games, Yohance A. P. Osborne & IS, Mathematics of Computation, volume 95, 2025 (online). doi:10.1090/mcom/4080.

Journal version arXiv version

Finite element approximation of time-dependent mean field games with nondifferentiable Hamiltonians, Yohance A. P. Osborne & IS, Numerische Mathematik, volume 157, pages 165-211, 2025. doi:10.1007/s00211-024-01447-2.

Journal version arXiv version

Analysis and numerical approximation of stationary second-order mean field game partial differential inclusions, Yohance A. P. Osborne & IS, SIAM Journal on Numerical Analysis, volume 62(1), pages 138-166, 2024. doi:10.1137/22M1519274.

Journal version Erratum arXiv version

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, volume 42(2), pages 1023-1049, 2022. doi:10.1093/imanum/draa103

Journal version arXiv version HAL version

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, volume 22, pages 315-364, 2022. doi:10.1007/s10208-021-09493-0

Journal version arXiv version

Unified analysis of discontinuous Galerkin and C0-interior penalty finite element methods for Hamilton–Jacobi–Bellman and Isaacs equations, E. L. Kawecki & IS, ESAIM Mathematical Modelling and Numerical Analysis, volume 55(2), pages 449-478, 2021. doi:10.1051/m2an/2020081

Journal version arXiv version

Simple and robust equilibrated flux a posteriori estimates for singularly perturbed reaction-diffusion problems, IS & M. Vohralik, ESAIM Mathematical Modelling and Numerical Analysis, volume 54(6), pages 1951-1973, 2020. doi:10.1051/m2an/2020034

Journal version arXiv version HAL version

Time-parallel iterative solvers for parabolic evolution equations, M. Neumüller & IS, SIAM Journal on Scientific Computing, volume 41(1), pages C28-C51, 2019, doi:10.1137/18M1172466.

Journal version arXiv version

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, volume 76(5), pages 967-983, 2018. doi:10.1016/j.camwa.2018.05.034.

Journal version arXiv version HAL version

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, volume 39(3), pages 1158-1179, 2018. doi:10.1093/imanum/dry035.

Journal version arXiv version HAL version

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. doi:10.1007/s10915-017-0428-5.

Journal version arXiv version HAL version

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(6), pages 2811-2834, 2017. doi:10.1137/16M1097626

Journal version arXiv version HAL version

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(3), pages 1009-1025, 2017. doi:10.1007/s10092-017-0217-4

Journal version arXiv version HAL version

Robust and efficient preconditioners for the discontinuous Galerkin time-stepping method, IS, IMA Journal of Numerical Analysis, volume 37(4), pages 1961-1985, 2017. doi:10.1093/imanum/drw050

Journal version arXiv version HAL version

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(4), pages 513–524, 2016.

Journal version

Discontinuous Galerkin finite element methods for time-dependent Hamilton–Jacobi–Bellman equations with Cordes coefficients, IS & E. Süli, Numerische Mathematik, volume 133(1), pages 141-176, 2016. doi:10.1007/s00211-015-0741-6

Journal version arXiv version

Discontinuous Galerkin finite element approximation of Hamilton–Jacobi–Bellman equations with Cordes coefficients, IS and E. Süli, SIAM Journal on Numerical Analysis, volume 52(2), pages 993–1016, 2014. doi:10.1137/130909536

Journal version

Discontinuous Galerkin finite element approximation of nondivergence form elliptic equations with Cordes coefficients, IS and E. Süli, SIAM Journal on Numerical Analysis, volume 51(4), pages 2088–2106, 2013. doi:10.1137/120899613

Journal version

On the convergence of finite element methods for Hamilton–Jacobi–Bellman equations, M. Jensen and IS, SIAM Journal on Numerical Analysis, volume 51(1), pages 137–162, 2013. doi:10.1137/110856198

Journal version arXiv version

Conference proceedings and book chapters

An introduction to the a posteriori error analysis of parabolic partial differential equations, IS, Advances in Applied Mechanics, volume 61, pages 239-286, 2025. doi:10.1016/bs.aams.2025.09.004

Published version arXiv version

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. doi:10.1515/9783110543599

Published version arXiv version HAL version

Stable Discontinuous Galerkin FEM without penalty parameters, L. John, M. Neilan & IS, Numerical Mathematics and Advanced Applications 2015, pages 165-173, Springer, 2016. doi:10.1007/978-3-319-39929-4_17

Published version arXiv version HAL version

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. doi:10.1007/978-3-642-33134-3_29

Published version arXiv version

Oberwolfach Reports

Convergence of adaptive discontinuous Galerkin and C0-interior penalty finite element methods for Hamilton–Jacobi–Bellman and Isaacs equations, E. L. Kawecki and IS, in Bartels, S., Brenner, S. C., Feng. X, & Neilan, M., Numerical Methods for fully nonlinear and related PDEs, Mathematisches Forschungsinstitut Oberwolfach Report 18(2), 1651-1674, 2022. doi:10.4171/OWR/2021/31

Link

Convergence of adaptive discontinuous Galerkin and C0-interior penalty finite element methods for Hamilton–Jacobi–Bellman and Isaacs equations, E. L. Kawecki and IS, in Boffi, D., Carstensen, C., Ern, A., Hu, J., Nonstandard Finite Element Methods, Mathematisches Forschungsinstitut Oberwolfach Report 18(1), 87-148, 2022. doi:10.4171/OWR/2021/3

Link

Discontinuous Galerkin finite element approximation of Hamilton—Jacobi—Bellman equations with Cordes coefficients, IS and Endre Süli, in Dahlke, S., Kutyniok, G., Stevenson, R. & Süli, E., New Discretization Methods for the Numerical Approximation of PDEs, Mathematisches Forschungsinstitut Oberwolfach Report 12(1), 87-185, 2015. doi:10.4171/OWR/2015/2

Link

Analysis and approximation of Hamilton—Jacobi—Bellman equations with Cordes coefficients, Smears, I. & Süli, E, in Cohen, A., Dahmen, W., DeVore, R., & Kunoth, A., Multiscale and High-Dimensional Problems, Mathematisches Forschungsinstitut Oberwolfach Report, 10(3), 2179-2257, 2014. doi: 10.4171/OWR/2013/39

Link

DPhil Thesis

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

Oxford Thesis Repository

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