Rates of convergence of finite element approximations of second-order mean field games with nondifferentiable Hamiltonians, Yohance A. P. Osborne & IS, submitted, 2025.
A posteriori error bounds for finite element approximations of steady-state mean field games, Yohance A. P. Osborne, IS & Harry Wells, submitted, 2025.
Regularization of stationary second-order mean field game partial differential inclusions, Yohance A. P. Osborne & IS, accepted for publication in SIAM Journal on Mathematical Analysis, 2025.
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. doi:10.1090/mcom/4080.
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.
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.
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
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
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
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.
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.
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.
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
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
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
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.
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
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
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
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
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
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
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
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
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
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
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
Discontinuous Galerkin finite element approximation of Hamilton–Jacobi–Bellman equations with Cordes coefficients, IS, DPhil Thesis, University of Oxford, 2015.