Osborne, Yohance A. P.; Smears, Iain Analysis and numerical approximation of stationary second-order mean field game partial differential inclusions. (English) Zbl 07794526 SIAM J. Numer. Anal. 62, No. 1, 138-166 (2024). MSC: 65N30 65N15 65N12 91A16 91-08 82C31 93E20 93C10 35D30 35A01 35A02 35Q89 35Q84 35Q93 PDFBibTeX XMLCite \textit{Y. A. P. Osborne} and \textit{I. Smears}, SIAM J. Numer. Anal. 62, No. 1, 138--166 (2024; Zbl 07794526) Full Text: DOI arXiv
Osborne, Yohance A. P.; Smears, Iain Near and full quasi-optimality of finite element approximations of stationary second-order mean field games. arXiv:2402.00685 Preprint, arXiv:2402.00685 [math.NA] (2024). MSC: 65N15 65N30 35Q89 BibTeX Cite \textit{Y. A. P. Osborne} and \textit{I. Smears}, ``Near and full quasi-optimality of finite element approximations of stationary second-order mean field games'', Preprint, arXiv:2402.00685 [math.NA] (2024) Full Text: arXiv OA License
Osborne, Yohance A. P.; Smears, Iain Finite element approximation of time-dependent Mean Field Games with non-differentiable Hamiltonians. arXiv:2306.13174 Preprint, arXiv:2306.13174 [math.NA] (2023). BibTeX Cite \textit{Y. A. P. Osborne} and \textit{I. Smears}, ``Finite element approximation of time-dependent Mean Field Games with non-differentiable Hamiltonians'', Preprint, arXiv:2306.13174 [math.NA] (2023) Full Text: arXiv OA License
Kawecki, Ellya L.; Smears, Iain Convergence of adaptive discontinuous Galerkin and \(C^0\)-interior penalty finite element methods for Hamilton-Jacobi-Bellman and Isaacs equations. (English) Zbl 1492.65314 Found. Comput. Math. 22, No. 2, 315-364 (2022). Reviewer: Calin Ioan Gheorghiu (Cluj-Napoca) MSC: 65N30 65N50 65N12 35J10 91A05 91A15 35Q91 91-08 PDFBibTeX XMLCite \textit{E. L. Kawecki} and \textit{I. Smears}, Found. Comput. Math. 22, No. 2, 315--364 (2022; Zbl 1492.65314) Full Text: DOI arXiv
Ern, Alexandre; Gudi, Thirupathi; Smears, Iain; Vohralík, Martin Equivalence of local- and global-best approximations, a simple stable local commuting projector, and optimal \(hp\) approximation estimates in \(\boldsymbol{H}(\operatorname{div})\). (English) Zbl 1517.65108 IMA J. Numer. Anal. 42, No. 2, 1023-1049 (2022). MSC: 65N30 65N50 65N15 65N12 35B65 35B45 PDFBibTeX XMLCite \textit{A. Ern} et al., IMA J. Numer. Anal. 42, No. 2, 1023--1049 (2022; Zbl 1517.65108) Full Text: DOI arXiv
Kawecki, Ellya L.; Smears, Iain Unified analysis of discontinuous Galerkin and \(C^0\)-interior penalty finite element methods for Hamilton-Jacobi-Bellman and Isaacs equations. (English) Zbl 1477.65225 ESAIM, Math. Model. Numer. Anal. 55, No. 2, 449-478 (2021). MSC: 65N30 65N15 65N12 35F21 35D35 35B65 49J30 35Q53 PDFBibTeX XMLCite \textit{E. L. Kawecki} and \textit{I. Smears}, ESAIM, Math. Model. Numer. Anal. 55, No. 2, 449--478 (2021; Zbl 1477.65225) Full Text: DOI arXiv
Smears, Iain; Vohralík, Martin Simple and robust equilibrated flux a posteriori estimates for singularly perturbed reaction-diffusion problems. (English) Zbl 1470.65199 ESAIM, Math. Model. Numer. Anal. 54, No. 6, 1951-1973 (2020). Reviewer: Chandrasekhar Salimath (Bengaluru) MSC: 65N30 65N15 65N50 35B35 35B25 PDFBibTeX XMLCite \textit{I. Smears} and \textit{M. Vohralík}, ESAIM, Math. Model. Numer. Anal. 54, No. 6, 1951--1973 (2020; Zbl 1470.65199) Full Text: DOI arXiv
Ern, Alexandre; Smears, Iain; Vohralík, Martin Equilibrated flux a posteriori error estimates in \(L^2(H^1)\)-norms for high-order discretizations of parabolic problems. (English) Zbl 1467.65092 IMA J. Numer. Anal. 39, No. 3, 1158-1179 (2019). Reviewer: Jan Giesselmann (Darmstadt) MSC: 65M60 65N30 65M15 PDFBibTeX XMLCite \textit{A. Ern} et al., IMA J. Numer. Anal. 39, No. 3, 1158--1179 (2019; Zbl 1467.65092) Full Text: DOI arXiv
Neumüller, Martin; Smears, Iain Time-parallel iterative solvers for parabolic evolution equations. (English) Zbl 1450.65106 SIAM J. Sci. Comput. 41, No. 1, C28-C51 (2019). Reviewer: Zhiming Chen (Beijing) MSC: 65M22 65M06 65F10 65F08 65Y05 65Y20 PDFBibTeX XMLCite \textit{M. Neumüller} and \textit{I. Smears}, SIAM J. Sci. Comput. 41, No. 1, C28--C51 (2019; Zbl 1450.65106) Full Text: DOI arXiv
Daniel, Patrik; Ern, Alexandre; Smears, Iain; Vohralík, Martin An adaptive \(hp\)-refinement strategy with computable guaranteed bound on the error reduction factor. (English) Zbl 1427.65356 Comput. Math. Appl. 76, No. 5, 967-983 (2018). MSC: 65N30 65N12 65N50 65N15 35J05 PDFBibTeX XMLCite \textit{P. Daniel} et al., Comput. Math. Appl. 76, No. 5, 967--983 (2018; Zbl 1427.65356) Full Text: DOI arXiv
Jensen, Max; Smears, Iain On the notion of boundary conditions in comparison principles for viscosity solutions. (English) Zbl 1404.35073 Kalise, Dante (ed.) et al., Hamilton-Jacobi-Bellman equations. Numerical methods and applications in optimal control. Based on the workshop “Numerical methods for Hamilton-Jacobi equations in optimal control and related fields”, Linz, Austria, November 21–25, 2016. Berlin: De Gruyter (ISBN 978-3-11-054263-9/hbk; 978-3-11-054359-9/ebook). Radon Series on Computational and Applied Mathematics 21, 143-154 (2018). MSC: 35B51 35D40 35J96 35F21 PDFBibTeX XMLCite \textit{M. Jensen} and \textit{I. Smears}, Radon Ser. Comput. Appl. Math. 21, 143--154 (2018; Zbl 1404.35073) Full Text: DOI arXiv
Smears, Iain Nonoverlapping domain decomposition preconditioners for discontinuous Galerkin approximations of Hamilton-Jacobi-Bellman equations. (English) Zbl 1385.65026 J. Sci. Comput. 74, No. 1, 145-174 (2018). Reviewer: Constantin Popa (Constanţa) MSC: 65F08 65F10 65N22 65N55 65N30 35J66 35F21 PDFBibTeX XMLCite \textit{I. Smears}, J. Sci. Comput. 74, No. 1, 145--174 (2018; Zbl 1385.65026) Full Text: DOI arXiv
Smears, Iain Robust and efficient preconditioners for the discontinuous Galerkin time-stepping method. (English) Zbl 1433.65224 IMA J. Numer. Anal. 37, No. 4, 1961-1985 (2017). MSC: 65M60 65M22 PDFBibTeX XMLCite \textit{I. Smears}, IMA J. Numer. Anal. 37, No. 4, 1961--1985 (2017; Zbl 1433.65224) Full Text: DOI arXiv
Ern, Alexandre; Smears, Iain; VohralÍk, Martin Guaranteed, locally space-time efficient, and polynomial-degree robust a posteriori error estimates for high-order discretizations of parabolic problems. (English) Zbl 1378.65165 SIAM J. Numer. Anal. 55, No. 6, 2811-2834 (2017). MSC: 65M15 65M60 35K20 PDFBibTeX XMLCite \textit{A. Ern} et al., SIAM J. Numer. Anal. 55, No. 6, 2811--2834 (2017; Zbl 1378.65165) Full Text: DOI arXiv
Ern, Alexandre; Smears, Iain; Vohralík, Martin Discrete \(p\)-robust \(\boldsymbol H(\mathrm{div})\)-liftings and a posteriori estimates for elliptic problems with \(H^{-1}\) source terms. (English) Zbl 1378.65173 Calcolo 54, No. 3, 1009-1025 (2017). Reviewer: Seenith Sivasundaram (Daytona Beach) MSC: 65N15 35J25 PDFBibTeX XMLCite \textit{A. Ern} et al., Calcolo 54, No. 3, 1009--1025 (2017; Zbl 1378.65173) Full Text: DOI arXiv
John, Lorenz; Neilan, Michael; Smears, Iain Stable discontinuous Galerkin FEM without penalty parameters. (English) Zbl 1352.65517 Karasözen, Bülent (ed.) et al., Numerical mathematics and advanced applications – ENUMATH 2015. Selected papers based on the presentations at the European conference, Ankara, Turkey, September 14–18, 2015. Cham: Springer (ISBN 978-3-319-39927-0/hbk; 978-3-319-39929-4/ebook). Lecture Notes in Computational Science and Engineering 112, 165-173 (2016). MSC: 65N30 PDFBibTeX XMLCite \textit{L. John} et al., Lect. Notes Comput. Sci. Eng. 112, 165--173 (2016; Zbl 1352.65517) Full Text: DOI arXiv
Antonietti, Paola F.; Houston, Paul; Smears, Iain A note on optimal spectral bounds for nonoverlapping domain decomposition preconditioners for \(hp\)-version discontinuous Galerkin methods. (English) Zbl 1350.65134 Int. J. Numer. Anal. Model. 13, No. 4, 513-524 (2016). Reviewer: Constantin Popa (Constanţa) MSC: 65N55 65N30 65F08 35J25 PDFBibTeX XMLCite \textit{P. F. Antonietti} et al., Int. J. Numer. Anal. Model. 13, No. 4, 513--524 (2016; Zbl 1350.65134) Full Text: Link
Smears, Iain; Süli, Endre Discontinuous Galerkin finite element methods for time-dependent Hamilton-Jacobi-Bellman equations with Cordes coefficients. (English) Zbl 1338.65229 Numer. Math. 133, No. 1, 141-176 (2016). Reviewer: Abdallah Bradji (Annaba) MSC: 65M60 35F21 65M12 65M15 65Y20 PDFBibTeX XMLCite \textit{I. Smears} and \textit{E. Süli}, Numer. Math. 133, No. 1, 141--176 (2016; Zbl 1338.65229) Full Text: DOI arXiv
Smears, Iain; Süli, Endre Discontinuous Galerkin finite element approximation of Hamilton-Jacobi-Bellman equations with Cordes coefficients. (English) Zbl 1304.65252 SIAM J. Numer. Anal. 52, No. 2, 993-1016 (2014). Reviewer: Basilis Kokkinis (Athens) MSC: 65N30 65N12 65N15 35J15 35J60 35J66 35D35 35F21 PDFBibTeX XMLCite \textit{I. Smears} and \textit{E. Süli}, SIAM J. Numer. Anal. 52, No. 2, 993--1016 (2014; Zbl 1304.65252) Full Text: DOI Link
Smears, Iain; Süli, Endre Discontinuous Galerkin finite element approximation of nondivergence form elliptic equations with Cordès coefficients. (English) Zbl 1278.65182 SIAM J. Numer. Anal. 51, No. 4, 2088-2106 (2013). Reviewer: Nicolae Pop (Baia Mare) MSC: 65N30 65N12 35J15 35R05 PDFBibTeX XMLCite \textit{I. Smears} and \textit{E. Süli}, SIAM J. Numer. Anal. 51, No. 4, 2088--2106 (2013; Zbl 1278.65182) Full Text: DOI Link
Jensen, M.; Smears, I. Finite element methods with artificial diffusion for Hamilton-Jacobi-Bellman equations. (English) Zbl 1267.65131 Cangiani, Andrea (ed.) et al., Numerical mathematics and advanced applications 2011. Proceedings of ENUMATH 2011, the 9th European conference on numerical mathematics and advanced applications, Leicester, UK, September 5–9, 2011. Berlin: Springer (ISBN 978-3-642-33133-6/hbk; 978-3-642-33134-3/ebook). 267-274 (2013). MSC: 65M60 PDFBibTeX XMLCite \textit{M. Jensen} and \textit{I. Smears}, in: Numerical mathematics and advanced applications 2011. Proceedings of ENUMATH 2011, the 9th European conference on numerical mathematics and advanced applications, Leicester, UK, September 5--9, 2011. Berlin: Springer. 267--274 (2013; Zbl 1267.65131) Full Text: DOI arXiv
Jensen, Max; Smears, Iain On the convergence of finite element methods for Hamilton-Jacobi-Bellman equations. (English) Zbl 1266.65166 SIAM J. Numer. Anal. 51, No. 1, 137-162 (2013). Reviewer: Abdallah Bradji (Annaba) MSC: 65M60 65M12 35D40 35K65 35K55 PDFBibTeX XMLCite \textit{M. Jensen} and \textit{I. Smears}, SIAM J. Numer. Anal. 51, No. 1, 137--162 (2013; Zbl 1266.65166) Full Text: DOI arXiv Link