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Scott Congreve

Journal Articles

1. S. Congreve and A. Hodson. A posteriori error analysis of the virtual element method for second-order quasilinear elliptic PDEs. Comput. Methods Appl. Math., 2025. Accepted.Zenodo10.5281/zenodo.16608856
2. S. Congreve, V. Dolejší, and S. Sakić. Error analysis for local discontinuous Galerkin semidiscretization of Richards' equation. IMA J. Numer. Anal., 45(1):580–630, 2025.DOI10.1093/imanum/drae013
3. V. Dolejší and S. Congreve. Goal-oriented error analysis of iterative Galerkin discretizations for nonlinear problems including linearization and algebraic errors. J. Comput. Appl. Math, 427:115134, 2023.DOI10.1016/j.cam.2023.115134
4. S. Congreve and P. Houston. Two-grid hp-version discontinuous Galerkin finite element methods for quasilinear elliptic PDEs on agglomerated coarse meshes. Adv. Comput. Math., 48, 2022. SpringerNature SharedIt.DOI10.1007/s10444-022-09968-w
5. S. Congreve, J. Gedicke, and I. Perugia. Robust adaptive hp discontinuous Galerkin finite element methods for the Helmholtz equation. SIAM J. Sci. Comput., 42(2):A1121–A1147, 2019.DOI10.1137/18M1207909
6. S. Congreve, P. Houston, and I. Perugia. Adaptive refinement for hp-version Trefftz discontinuous Galerkin methods for the homogeneous Helmholtz problem. Adv. Comput. Math., 45(1):361–393, 2019.DOI10.1007/s10444-018-9621-9
7. S. Congreve and T. P. Wihler. Iterative Galerkin discretizations for strongly monotone problems. J. Comput. Appl. Math., 311:457–472, 2017.DOI10.1016/j.cam.2016.08.014
8. S. Congreve and P. Houston. Two-grid hp-version discontinuous Galerkin finite element methods for quasi-Newtonian flows. Int. J. Numer. Anal. Model., 11(3):496–524, 2014.
9. S. Congreve, P. Houston, E. Süli, and T. P. Wihler. Discontinuous Galerkin finite element approximation of quasilinear elliptic boundary value problems II: Strongly monotone quasi-Newtonian flows. IMA J. Numer. Anal., 33(4):1386–1415, 2013.DOI10.1093/imanum/drs046
10. S. Congreve, P. Houston, and T. P. Wihler. Two-grid hp-version discontinuous Galerkin finite element methods for second-order quasilinear elliptic PDEs. J. Sci. Comput., 55(2):471–497, 2013.DOI10.1007/s10915-012-9644-1

Conference Proceedings

1. S. Sakić and S. Congreve. Numerical study of a discontinuous Galerkin method for a degenerate parabolic equation. In A. Sequeira, A. Silvestre, S. Valtchev, and J. Janela, editors, Numerical Mathematics and Advanced Applications ENUMATH 2023, Volume 2, Lecture Notes in Computational Science and Engineering, pages 331–339. Lisbon, Portugal, 2025. Springer.DOI10.1007/978-3-031-86169-7_34
2. S. Congreve and P. Houston. Two-grid hp-DGFEMs on agglomerated coarse meshes. Proc. Appl. Math. Mech., 19:e201900175, 2019.DOI10.1002/pamm.201900175
3. S. Congreve, J. Gedicke, and I. Perugia. Numerical investigation of the conditioning for plane wave discontinuous Galerkin methods. In F. Radu, K. Kumar, I. Berre, J. Nordbotten, and I. Pop, editors, Numerical Mathematics and Advanced Applications ENUMATH 2017, volume 126 of Lecture Notes in Computational Science and Engineering, pages 493–500. Voss, Norway, 2017. Springer.DOI10.1007/978-3-319-96415-7_44
4. S. Congreve and P. Houston. Two-grid hp-DGFEM for second order quasi-linear elliptic PDEs based on a single Newton iteration. In J. Li and H. Yang, editors, Proceedings of the 8th International Conference on Scientific Computing and Applications, volume 586 of Contemporary Mathematics, pages 135–142. University of Nevada, Las Vegas, 2013. AMS.DOI10.1090/conm/586/11629
5. S. Congreve, P. Houston, and T. P. Wihler. Two-grid hp-version discontinuous Galerkin finite element methods for quasi-Newtonian flows. In A. Cangiani, R. Davidchack, E. Georgoulis, A. Gorban, J. Levesley, and M. Tretyakov, editors, Numerical Mathematics and Advanced Applications ENUMATH 2011, Lecture Notes in Computational Science and Engineering, pages 341–349. University of Leicester, Leicester, UK, 2012. Springer.DOI10.1007/978-3-642-33134-3_37
6. S. Congreve, P. Houston, and T. P. Wihler. Two-grid hp-version DGFEMs for strongly monotone second-order quasilinear elliptic PDEs. Proc. Appl. Math. Mech., 11:3–6, 2011.DOI10.1002/pamm.201110002

Theses

1. S. Congreve. Two-grid hp-Version discontinuous Galerkin finite element methods for quasilinear PDEs. PhD thesis, University of Nottingham, Nottingham, UK, 2014. Nottingham eThesis.
2. S. Congreve. A posteriori error analysis of hp-adaptive finite element methods for second-order quasi-linear PDEs. Master's thesis, University of Nottingham, Nottingham, UK, 2010.