A posteriori error bounds for finite element approximations of time-dependent mean field games.

Iain Smears https://orcid.org/0000-0003-0005-4327

Iain Smears Harry Wells A posteriori error bounds for finite element approximations of time-dependent mean field games. 2026 June abs/2606.23613 CoRR https://doi.org/10.48550/arXiv.2606.23613 db/journals/corr/corr2606.html#abs-2606-23613 streams/journals/corr

Thomas Hall Iain Smears Endre Süli Harry Wells The Effect of Quadrature on the Convergence of Policy Iteration for Hamilton-Jacobi-Bellman Equations. 2026 June abs/2606.24806 CoRR https://doi.org/10.48550/arXiv.2606.24806 db/journals/corr/corr2606.html#abs-2606-24806 streams/journals/corr

Yohance A. P. Osborne Iain Smears Near and full quasi-optimality of finite element approximations of stationary second-order mean field games. 525-555 2025 95 Math. Comput. 358 https://doi.org/10.1090/mcom/4080 db/journals/moc/moc95.html#OsborneS25 streams/journals/moc

Yohance A. P. Osborne Iain Smears Finite element approximation of time-dependent mean field games with nondifferentiable Hamiltonians. 165-211 2025 February 157 Numerische Mathematik 1 https://doi.org/10.1007/s00211-024-01447-2 db/journals/nm/nm157.html#OsborneS25 streams/journals/nm

Yohance A. P. Osborne Iain Smears Regularization of Stationary Second-Order Mean Field Game Partial Differential Inclusions. 5189-5215 2025 57 SIAM J. Math. Anal. 5 https://doi.org/10.1137/24m1686401 db/journals/siamma/siamma57.html#OsborneS25 streams/journals/siamma

Yohance A. P. Osborne Iain Smears Harry Wells A posteriori error bounds for finite element approximations of steady-state mean field games. 2025 February abs/2502.14687 CoRR https://doi.org/10.48550/arXiv.2502.14687 db/journals/corr/corr2502.html#abs-2502-14687 streams/journals/corr

Yohance A. P. Osborne Iain Smears Rates of convergence of finite element approximations of second-order mean field games with nondifferentiable Hamiltonians. 2025 June abs/2506.03039 CoRR https://doi.org/10.48550/arXiv.2506.03039 db/journals/corr/corr2506.html#abs-2506-03039 streams/journals/corr

Iain Smears On the efficiency of a posteriori error estimators for parabolic partial differential equations in the energy norm. 2025 July abs/2507.13188 CoRR https://doi.org/10.48550/arXiv.2507.13188 db/journals/corr/corr2507.html#abs-2507-13188 streams/journals/corr

Iain Smears An introduction to the a posteriori error analysis of parabolic partial differential equations. 2025 November abs/2511.00245 CoRR https://doi.org/10.48550/arXiv.2511.00245 db/journals/corr/corr2511.html#abs-2511-00245 streams/journals/corr

Yohance A. P. Osborne Iain Smears Analysis and Numerical Approximation of Stationary Second-Order Mean Field Game Partial Differential Inclusions. 138-166 2024 February 62 SIAM J. Numer. Anal. 1 https://doi.org/10.1137/22m1519274 db/journals/siamnum/siamnum62.html#OsborneS24

Yohance A. P. Osborne Iain Smears Erratum: Analysis and Numerical Approximation of Stationary Second-Order Mean Field Game Partial Differential Inclusions. 2415-2417 2024 62 SIAM J. Numer. Anal. 5 https://doi.org/10.1137/24m165123x db/journals/siamnum/siamnum62.html#OsborneS24a streams/journals/siamnum

Yohance A. P. Osborne Iain Smears Near and full quasi-optimality of finite element approximations of stationary second-order mean field games. 2024 abs/2402.00685 CoRR https://doi.org/10.48550/arXiv.2402.00685 db/journals/corr/corr2402.html#abs-2402-00685

Yohance A. P. Osborne Iain Smears Finite element approximation of time-dependent Mean Field Games with non-differentiable Hamiltonians. 2023 abs/2306.13174 CoRR https://doi.org/10.48550/arXiv.2306.13174 db/journals/corr/corr2306.html#abs-2306-13174

Ellya L. Kawecki Iain Smears Convergence of Adaptive Discontinuous Galerkin and C0-Interior Penalty Finite Element Methods for Hamilton-Jacobi-Bellman and Isaacs Equations. 315-364 2022 22 Found. Comput. Math. 2 https://doi.org/10.1007/s10208-021-09493-0 db/journals/focm/focm22.html#KaweckiS22

Yohance A. P. Osborne Iain Smears Analysis and Numerical Approximation of Stationary Second-Order Mean Field Game Partial Differential Inclusions. 2022 abs/2209.00303 CoRR https://doi.org/10.48550/arXiv.2209.00303 db/journals/corr/corr2209.html#abs-2209-00303

Ellya L. Kawecki Iain Smears Unified analysis of discontinuous Galerkin and C0-interior penalty finite element methods for Hamilton-Jacobi-Bellman and Isaacs equations. 2020 abs/2006.07202 CoRR https://arxiv.org/abs/2006.07202 db/journals/corr/corr2006.html#abs-2006-07202

Ellya L. Kawecki Iain Smears Convergence of adaptive discontinuous Galerkin and C0-interior penalty finite element methods for Hamilton-Jacobi-Bellman and Isaacs equations. 2020 abs/2006.07215 CoRR https://arxiv.org/abs/2006.07215 db/journals/corr/corr2006.html#abs-2006-07215

Martin Neumüller Iain Smears Time-Parallel Iterative Solvers for Parabolic Evolution Equations. C28-C51 2019 41 SIAM J. Sci. Comput. 1 https://doi.org/10.1137/18M1172466 db/journals/siamsc/siamsc41.html#NeumullerS19

Alexandre Ern Thirupathi Gudi Iain Smears Martin Vohralík Equivalence of local-and global-best approximations, a simple stable local commuting projector, and optimal hp approximation estimates in H(div). 2019 abs/1908.08158 CoRR http://arxiv.org/abs/1908.08158 db/journals/corr/corr1908.html#abs-1908-08158

Patrik Daniel Alexandre Ern Iain Smears Martin Vohralík An adaptive hp-refinement strategy with computable guaranteed bound on the error reduction factor. 967-983 2018 76 Comput. Math. Appl. 5 https://doi.org/10.1016/j.camwa.2018.05.034 db/journals/cma/cma76.html#DanielESV18

Iain Smears Nonoverlapping Domain Decomposition Preconditioners for Discontinuous Galerkin Approximations of Hamilton-Jacobi-Bellman Equations. 145-174 2018 74 J. Sci. Comput. 1 https://doi.org/10.1007/s10915-017-0428-5 db/journals/jscic/jscic74.html#Smears18

Alexandre Ern Iain Smears Martin Vohralík Guaranteed, Locally Space-Time Efficient, and Polynomial-Degree Robust a Posteriori Error Estimates for High-Order Discretizations of Parabolic Problems. 2811-2834 2017 55 SIAM J. Numer. Anal. 6 https://doi.org/10.1137/16M1097626 db/journals/siamnum/siamnum55.html#ErnSV17

Iain Smears Endre Süli Discontinuous Galerkin finite element methods for time-dependent Hamilton-Jacobi-Bellman equations with Cordes coefficients. 141-176 2016 133 Numerische Mathematik 1 https://doi.org/10.1007/s00211-015-0741-6 db/journals/nm/nm133.html#SmearsS16

Lorenz John Michael Neilan Iain Smears Stable Discontinuous Galerkin FEM Without Penalty Parameters. 165-173 2015 ENUMATH https://doi.org/10.1007/978-3-319-39929-4_17 conf/enumath/2015 db/conf/enumath/enumath2015.html#JohnNS15

Iain Smears Endre Süli Discontinuous Galerkin Finite Element Approximation of Hamilton-Jacobi-Bellman Equations with Cordes Coefficients. 993-1016 2014 52 SIAM J. Numer. Anal. 2 https://doi.org/10.1137/130909536 db/journals/siamnum/siamnum52.html#SmearsS14

Max Jensen Iain Smears On the Convergence of Finite Element Methods for Hamilton-Jacobi-Bellman Equations. 137-162 2013 51 SIAM J. Numer. Anal. 1 https://doi.org/10.1137/110856198 db/journals/siamnum/siamnum51.html#JensenS13

Iain Smears Endre Süli Discontinuous Galerkin Finite Element Approximation of Nondivergence Form Elliptic Equations with Cordès Coefficients. 2088-2106 2013 51 SIAM J. Numer. Anal. 4 https://doi.org/10.1137/120899613 db/journals/siamnum/siamnum51.html#SmearsS13

Patrik Daniel Alexandre Ern Thirupathi Gudi Thomas Hall Max Jensen Lorenz John Ellya L. Kawecki Michael Neilan Martin Neumüller Yohance A. P. Osborne Endre Süli Martin Vohralík Harry Wells