Publications by E. H. Georgoulis

 

Monograph

 

1.     A. Cangiani, Z. Dong, E. H. Georgoulis and P. Houston.
hp–Version discontinuous Galerkin methods on polygonal and polyhedral meshes. Springer Briefs in Mathematics

 

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Textbook

 

1.     E. H. Georgoulis.

Numerical Analysis of Partial Differential Equations (in Greek). Kallipos Open Academic Editions Repository (open access).



Edited Volumes

  1. E. H. Georgoulis, A. Iske, and J. Levesley (eds.)
    Approximation Algorithms for Complex Systems. Springer Proceedings in Mathematics, Vol. 3, Springer-Verlag, Berlin (2011).

  2. A. Cangiani , R. L. Davidchack , E. H. Georgoulis, A. N. Gorban , J. Levesley , M. V. Tretyakov (eds.)
    Numerical Mathematics and Advanced Applications 2011: Proceedings of ENUMATH 2011, the 9th European Conference on Numerical Mathematics and Advanced Applications, Leicester, September 2011. Springer (2013).

  3. G. R. Barrenechea, F. Brezzi, A. Cangiani , and E. H. Georgoulis (eds.)
    Building Bridges: Connections and Challenges in Modern Approaches to Numerical Partial Differential Equations. Lecture Notes in Computational Science and Engineering, Springer (2016).

Chapters in peer-reviewed books

  1. E. H. Georgoulis, E. Hall and C. Makridakis.
    A posteriori error control for discontinuous Galerkin methods for first order hyperbolic problems. In Recent Developments in Discontinuous Galerkin Finite Element Methods for Partial Differential Equations: 2012 John H Barrett Memorial Lectures, Springer (2014).

  2. P. F. Antonietti, A. Cangiani, J. Collis, Z. Dong, E. H. Georgoulis, S. Giani and P. Houston.
    Review of Discontinuous Galerkin Finite Element Methods for Partial Differential Equations on Complicated Domains. In Building Bridges: Connections and Challenges in Modern Approaches to Numerical Partial Differential Equations. Lecture Notes in Computational Science and Engineering 114, Springer (2016).

  3. G. Akrivis and E. H. Georgoulis.
    Implicit-Explicit multistep methods for non-linear convection-diffusion equations. In Boundary and Interior Layers, Computational and Asymptotic Methods BAIL 2018 pp 59–81. Lecture Notes in Computational Science and Engineering 135, Springer (2020).

  4. T. Barry, A. Cangiani, S. P. Cox, E. H. Georgoulis.
    An a posteriori error estimator for discontinuous Galerkin discretisations of convection-diffusion problems with application to Earth's mantle convection simulations. Advances in Applied Mechanics 61, 347-405 (2025). PDF

Articles in peer-reviewed journals

  1. E. H. Georgoulis and E. Süli.
    Optimal error estimates for the hp-version interior penalty discontinuous Galerkin finite element method. IMA Journal of Numerical Analysis 25(1) pp. 205-220 (2005).

  2. E. H. Georgoulis.
    hp-version interior penalty discontinuous Galerkin finite element methods on anisotropic meshes. International Journal of Numerical Analysis and Modeling 3(1) pp. 52-79 (2006).

  3. E. H. Georgoulis and A. Lasis.
    A note on the design of hp-version interior penalty discontinuous Galerkin finite element methods for degenerate problems. IMA Journal of Numerical Analysis 26(2) pp.381-390 (2006).

  4. R. Brownlee, E. H. Georgoulis and J. Levesley.
    Extending the range of error estimates for radial approximation in Euclidean space and on spheres. SIAM Journal on Mathematical Analysis 39(2) pp. 554-564 (2007).

  5. E. H. Georgoulis, E. Hall and P. Houston.
    Discontinuous Galerkin methods for advection-diffusion-reaction problems on anisotropically refined meshes. SIAM Journal on Scientific Computing 30(1) pp. 246-271 (2007).

  6. E. H. Georgoulis, E. Hall and P. Houston.
    Discontinuous Galerkin methods on hp-anisotropic meshes I: a priori error analysis. International Journal of Computing Science and Mathematics 1(2-3) pp. 221-244 (2007).

  7. E. H. Georgoulis.
    Inverse-type estimates on hp-finite element spaces and applications. Mathematics of Computation 77 pp. 201-219 (2008).

  8. E. H. Georgoulis and D. Loghin.
    Norm preconditioners for discontinuous Galerkin hp-finite element methods. SIAM Journal on Scientific Computing 30(5) pp. 2447-2465 (2008).

  9. E. H. Georgoulis, E. Hall and P. Houston.
    Discontinuous Galerkin methods on hp-anisotropic meshes II: a posteriori error analysis and adaptivity. Applied Numerical Mathematics 59(9) pp. 2179-2194 (2009).

  10. E. H. Georgoulis and P. Houston.
    Discontinuous Galerkin methods for the biharmonic problem. IMA Journal of Numerical Analysis 29(3) pp. 573-594 (2009).

  11. E. H. Georgoulis, E. Hall and J. M. Melenk.
    On the suboptimality of the p-version interior penalty discontinuous Galerkin method. Journal of Scientific Computing 42(1) pp. 54-67 (2010).

  12. T. Aboiyar, E. H. Georgoulis, and A. Iske.
    Adaptive ADER methods using kernel-based polyharmonic spline WENO reconstruction. SIAM Journal on Scientific Computing 32(6) pp. 3251-3277 (2010).

  13. E. H. Georgoulis, P. Houston and J.M. Virtanen.
    An a posteriori error indicator for discontinuous Galerkin approximations of fourth order elliptic problems. IMA Journal of Numerical Analysis 31(1) pp. 281-298 (2011).

  14. E. H. Georgoulis, O. Lakkis and J.M. Virtanen.
    A posteriori error control for discontinuous Galerkin methods for parabolic problems. SIAM Journal on Numerical Analysis 49(2) pp. 427-458 (2011).

  15. A. Demlow and E. H. Georgoulis.
    Pointwise a posteriori error control for discontinuous Galerkin methods for elliptic problems. SIAM Journal on Numerical Analysis 50(5) pp. 2159-2181 (2012).

  16. E. H. Georgoulis, O. Lakkis and C. Makridakis.
    A posteriori L∞(L2)-error bounds in finite element approximation of the wave equation. IMA Journal of Numerical Analysis 33(4) pp. 1245-1264 (2013). PDF

  17. E. H. Georgoulis, J. Levesley and F. Subhan.
    Multilevel sparse kernel-based interpolation. SIAM Journal on Scientific Computing 35(2) pp. A815-A831 (2013). PDF

  18. M. Arioli, E. H. Georgoulis and D. Loghin.
    Stopping criteria for adaptive finite element solvers. SIAM Journal on Scientific Computing 35(3) pp. A1537-A1559 (2013). PDF

  19. A. Cangiani, J. Chapman, E. H. Georgoulis and M. Jensen.
    On the stability of continuous-discontinuous Galerkin methods for advection-diffusion-reaction problems. Journal of Scientific Computing 57(2), pp. 313-330 (2013). PDF

  20. D. Elfverson, E. H. Georgoulis and A. Målqvist.
    An adaptive discontinuous Galerkin multiscale method for elliptic problems. SIAM Multiscale Modelling and Simulation 11(3) pp. 747-765 (2013). PDF

  21. A. Cangiani, E. H. Georgoulis and M. Jensen.
    Discontinuous Galerkin methods for mass transfer through semi-permeable membranes. SIAM Journal on Numerical Analysis 51(5) pp. 2911-2934 (2013). PDF

  22. D. Elfverson, E. H. Georgoulis, A. Målqvist and D. Peterseim.
    Convergence of a discontinuous Galerkin multiscale method. SIAM Journal on Numerical Analysis 51(6) pp. 3351-3372 (2013). PDF

  23. A. Cangiani, E. H. Georgoulis and S. Metcalfe.
    Adaptive discontinuous Galerkin methods for non-stationary convection-diffusion problems. IMA Journal of Numerical Analysis 34 pp. 1578-1597 (2014). PDF

  24. E. H. Georgoulis and C. Makridakis.
    On a posteriori error control for the Allen-Cahn problem. Mathematical Methods in the Applied Sciences 37(2) pp. 173-179, (2014). PDF

  25. A. Cangiani, J. Chapman, E. H. Georgoulis and M. Jensen.
    On local super-penalization of interior penalty discontinuous Galerkin methods. International Journal of Numerical Analysis and Modeling 11(3) pp. 478-495 (2014). PDF

  26. A. Cangiani, E. H. Georgoulis and P. Houston.
    hp–Version discontinuous Galerkin methods on polygonal and polyhedral meshes. Mathematical Models and Methods in Applied Sciences 24(10) pp. 2009 (2014). PDF

  27. E. H. Georgoulis and J. M. Virtanen.
    Adaptive discontinuous Galerkin approximations to fourth order parabolic problems. Mathematics of Computation 84, pp. 2163–2190 (2015). PDF

  28. A. Cangiani, E. H. Georgoulis and M. Jensen.
    Discontinuous Galerkin methods for fast reactive mass transfer through semi-permeable membranes. Applied Numerical Mathematics 104 pp. 3-14 (2016). PDF

  29. E. H. Georgoulis, O. Lakkis, C. Makridakis and J. Virtanen.
    A posteriori error estimates for leap-frog and cosine methods for second order evolution problems. SIAM Journal on Numerical Analysis. 54(1), pp. 120--136 (2016). PDF

  30. A. Cangiani, Z. Dong, E. H. Georgoulis and P. Houston.
    hp–Version discontinuous Galerkin methods for advection-diffusion-reaction problems on polytopic meshes. ESAIM: Mathematical Modelling and Numerical Analysis. 50(3) pp. 699-725, (2016). PDF

  31. A. Cangiani, E. H. Georgoulis, I. Kyza and S. Metcalfe.
    Adaptivity and blow-up detection for nonlinear evolution problems. SIAM Journal on Scientific Computing. 38(6) pp. A3833–A3856, (2016). PDF

  32. L. Banjai, E. H. Georgoulis and O. Lijoka.
    A Trefftz polynomial space-time discontinuous Galerkin method for the second order wave equation. SIAM Journal on Numerical Analysis. 55(1), pp.63–86, (2017). PDF

  33. A. Cangiani, E. H. Georgoulis, T. Pryer and O. J. Sutton.
    A posteriori error estimates for the virtual element method. Numerische Mathematik 137(4) pp.857--893 (2017). PDF

  34. A. Cangiani, Z. Dong, and E. H. Georgoulis.
    hp–Version space-time discontinuous Galerkin methods for parabolic problems on prismatic meshes. SIAM Journal on Scientific Computing 39(4) pp.A1251–A1279 (2017).
    Corrigendum, SIAM Journal on Scientific Computing 48(1) pp.A418-A424 (2026). [Complete Corrected version PDF]

  35. E. H. Georgoulis and T. Pryer.
    Analysis of discontinuous Galerkin methods using mesh-dependent norms and applications to problems with rough data. Calcolo 54(4), pp. 1533 -- 1551 (2017). PDF

  36. E. H. Georgoulis and T. Pryer.
    Recovered Finite Element Methods. Computer Methods in Applied Mechanics and Engineering 332, pp. 303 – 324 (2018). PDF

  37. C. Kreuzer and E. H. Georgoulis.
    Convergence of adaptive discontinuous Galerkin methods. Mathematics of Computation 87(314) pp. 2611 – 2640 (2018).
    Corrigendum, Mathematics of Computation 90, pp. 637 – 640 (2021).  [Complete Corrected version PDF]

  38. A. Cangiani, E. H. Georgoulis, and Y. Sabawi.
    Adaptive discontinuous Galerkin methods for elliptic interface problems. Mathematics of Computation 87(314) pp. 2675 – 2707 (2018). PDF

  39. A. Cangiani, E. H. Georgoulis, A. Yu. Morozov, and O. J. Sutton.
    Revealing new dynamical patterns in a reaction-diffusion model with cyclic competition via a novel computational framework. Proceedings of the Royal Society A 474(2213). PDF

  40. Z. Dong, E. H. Georgoulis, J. Levesley and F. Usta.
    A multilevel sparse kernel-based stochastic collocation finite element method for elliptic problems with random coefficients. Computers and Mathematics with Applications 76 pp. 1950 -- 1965 (2018). PDF

  41. E. H. Georgoulis, E. Hall and C. Makridakis.
    An a posteriori error bound for discontinuous Galerkin approximations of convection-diffusion problems. IMA Journal of Numerical Analysis 39(1) pp. 34--60 (2019). PDF

  42. A. Cangiani, E. H. Georgoulis, S. Giani, S. Metcalfe.
    hp-adaptive discontinuous Galerkin methods for non-stationary convection-diffusion problems. Computers and Mathematics with Applications no 9, pp.3090--3104 (2019). PDF

  43. A. Cangiani, E. H. Georgoulis, and Y. Sabawi.
    Convergence of an adaptive discontinuous Galerkin method for elliptic interface problems. Journal of Computational and Applied Mathematics 367, 112397, 15pp (2020). PDF

  44. A. Cangiani, E. H. Georgoulis, and M. Sabawi.
    A posteriori error analysis for implicit–explicit hp-discontinuous Galerkin timestepping methods for semilinear parabolic problems. Journal of Scientific Computing 82(2), Paper No. 26, 24 pp. (2020). PDF

  45. Z. Dong, E. H. Georgoulis and T. Pryer.
    Recovered Finite Element Methods on polygonal and polyhedral meshes. ESAIM: Mathematical Modelling and Numerical Analysis 54, no. 4, pp.1309–1337 (2020). PDF

  46. K. Chrysafinos, E. H. Georgoulis, and D. Plaka.
    A posteriori error estimates for the Allen-Cahn problem. SIAM Journal on Numerical Analysis 58(5), pp.2662–2683 (2020). PDF

  47. A. Cangiani, P. Chatzipandelidis, G. Diwan, E. H. Georgoulis.
    A virtual element method for quasilinear elliptic problems. IMA Journal of Numerical Analysis 40 (4), pp.2450--2472 (2020). PDF

  48. E. H. Georgoulis.
    Hypocoercivity-compatible finite element methods for the long-time computation of Kolmogorov's equation. SIAM Journal on Numerical Analysis 59(1) pp.173-194 (2021). PDF

  49. A. Cangiani, E. H. Georgoulis, and O. J. Sutton.
    Adaptive non-hierarchical Galerkin methods for parabolic problems with application to moving mesh and virtual element methods. Mathematical Models and Methods in Applied Sciences 31(4) pp. 711--751 (2021). PDF

  50. E. H. Georgoulis, O. Lakkis, and T. P. Wihler.
    A posteriori error bounds for fully-discrete hp-discontinuous Galerkin timestepping methods for parabolic problems. Numerische Mathematik 148(2) pp.363–386 (2021). PDF

  51. Z. Dong, E. H. Georgoulis, and T. Kappas.
    GPU-accelerated discontinuous Galerkin methods on polytopic meshes. SIAM Journal on Scientific Computing 43(4) pp. C312–C334 (2021). PDF

  52. A. Cangiani, Z. Dong, and E. H. Georgoulis.
    hp–Version discontinuous Galerkin methods on essentially arbitrarily-shaped elements. Mathematics of Computation 91 pp. 1-35 (2021). PDF

  53. Z. Dong, and E. H. Georgoulis.
    Robust interior penalty discontinuous Galerkin methods. Journal of Scientific Computing 92, no. 57 (2022). PDF

  54. E. H. Georgoulis, M. Loulakis and A. Tsiourvas.
    Discrete gradient flow approximations of high dimensional evolution partial differential equations via Deep Neural Networks. Communications in Nonlinear Science and Numerical Simulation, 117, 106893 (2023). PDF

  55. A. Cangiani, Z. Dong, and E. H. Georgoulis.
    A posteriori error estimates for discontinuous Galerkin methods on polygonal and polyhedral meshes. SIAM Journal on Numerical Analysis, 61(5) (2023). PDF

  56. E. H. Georgoulis and C. G. Makridakis.
    Lower bounds, elliptic reconstruction, and a posteriori error control of parabolic problems. IMA Journal of Numerical Analysis 43 (6) (2023).

  57. G. R. Barrenechea, E. H. Georgoulis, T. Pryer and A. Veeser.
    A nodally bound-preserving finite element method. IMA Journal of Numerical Analysis, 44(4) pp. 2198–2219 (2024). PDF

  58. K. Chrysafinos, E. H. Georgoulis and V. D. Papadopoulos.
    Mesh-dependent L2-like norm a posteriori error estimates for elliptic problems with non-essential boundary conditions. Journal of Scientific Computing, 100 (1) no. 8 (2024). PDF

  59. E. H. Georgoulis, E. J. C. Hall and C. G. Makridakis.
    On a posteriori error estimation for Runge-Kutta discontinuous Galerkin methods for linear hyperbolic problems. Studies in Applied Mathematics, 153(4) (2024). PDF

  60. Z. Dong, E. H. Georgoulis and P. J. Herbert.
    A hypocoercivity-exploiting stabilised finite element method for Kolmogorov equation. SIAM Journal on Numerical Analysis, 65(3) (2025). PDF

  61. R. E. Fernandes, E. H. Georgoulis, and A. Paganini.
    Level-set shape optimization via polytopic discontinuous Galerkin methods. SIAM Journal on Scientific Computing 47(5) B1293-B1315 (2025). PDF

  62. E. H. Georgoulis, A. Papapantoleon and C. Smaragdakis.
    A deep implicit-explicit minimizing movement method for option pricing in jump-diffusion models. Communications in Nonlinear Science and Numerical Simulation 109709 (2026). PDF

  63. E. H. Georgoulis, C. G. Makridakis, and T. Pryer.
    Babuška-Osborn techniques in discontinuous Galerkin methods: L2-norm error estimates for unstructured meshes. Submitted for publication.

  64. Z. Dong, E. H. Georgoulis, and P. J. Herbert.
    Asymptotic numerical hypocoercivity of the space-time discontinuous Galerkin method for Kolmogorov equation.  Submitted for publication. PDF

  65. L. Banjai, E. H. Georgoulis, and B. Hennessy.
    Space-time finite element methods for nonlinear wave equations via elliptic regularisation. Submitted for publication. PDF

  66. S. Zafeiris, E. H. Georgoulis, and G. Papadakis.
    Parallel nodal interior-penalty discontinuous Galerkin methods for the subsonic compressible Navier-Stokes equations: applications to vortical flows and VIV problems. Submitted for publication. PDF

  67. Z. Dong, E. H. Georgoulis, L. Mascotto, and Z. Wang.
    A posteriori error analysis and adaptivity of a space-time finite element method for the wave equation in second order formulation. Submitted for publication. PDF

  68. A. Amiri, G. R. Barrenechea, E. H. Georgoulis, and T. Pryer.
    A nodally bound-preserving composite discontinuous Galerkin method on polytopic meshes. Submitted for publication. PDF

  69. E. H. Georgoulis, and P. Paraschis.
    hp-Version robust interior penalty discontinuous Galerkin methods for the p-Laplacian on simplicial and on essentially arbitrarily-shaped element meshes. Submitted for publication. PDF

Contributions in conference proceedings:

  1. E. H. Georgoulis and D. Loghin.
         Krylov-Subspace preconditioners for discontinuous Galerkin finite element methods. ECCOMAS CFD 2006 Proceedings.

  2. A. Cangiani, E. H. Georgoulis and M. Jensen.
    Continuous and discontinuous finite element methods for convection-diffusion problems: a comparison. In G. Lube and G. Rapin, editors, Proceedings of the International Conference on Boundary and Interior Layers (BAIL) - Computational and Asymptotic Methods, 2006.

  3. P. Houston, E. H. Georgoulis, and E. Hall.
    Adaptivity and a posteriori error estimation For DG methods on anisotropic meshes. In G. Lube and G. Rapin, editors, Proceedings of the International Conference on Boundary and Interior Layers (BAIL) - Computational and Asymptotic Methods, 2006. 

  4. T. Aboiyar, E. H. Georgoulis, and A. Iske.
    High order WENO finite volume schemes using polyharmonic spline reconstruction. Proceedings of the International Conference on Numerical Analysis and Approximation Theory 2006, Cluj-Napoca, Romania.

  5. I. Spisso, A. Rona, and E. H. Georgoulis.
    Towards a monotonicity-preserving inviscid wall boundary condition for aeroacoustics. Proceedings of the 15th AIAA/CEAS Aeroacoustics Conference, Miami, FL, USA, 2009.

  6. E. H. Georgoulis, and O. Lakkis.
    A posteriori error bounds for discontinuous Galerkin methods for quasilinear parabolic problems. In G. Kreiss, P.Lötstedt, A. Målqvist, M. Neytcheva, (eds.), ENUMATH '09 Proceedings, Uppsala, Springer, 2010.

  7. E. H. Georgoulis.
    Discontinuous Galerkin methods for linear problems; an introduction. In E. H. Georgoulis, A. Iske, and J. Levesley (eds.), Approximation Algorithms for Complex Systems, Springer Proceedings in Mathematics, Vol. 3, Springer-Verlag, Berlin, 2011.

  8. A. Cangiani, E. H. Georgoulis and M. Jensen.
    Discontinuous Galerkin methods for convection-diffusion problems modelling mass transfer through semipermeable membranes. Proceedings of the Congress on Numerical Methods in Engineering, Coimbra, 2011.

  9. A. Cangiani, J. Chapman, E. H. Georgoulis and M. Jensen.
    Implementation of the continuous-discontinuous Galerkin finite element method. In A. Cangiani, R. Davidchack, E. H. Georgoulis, A. Gorban, J. Levesley, M. Tretyakov (eds.), ENUMATH '11 Proceedings, Leicester, Springer, 2013.

  10. E. H. Georgoulis, J. Levesley and F. Subhan. https://arxiv.org/abs/2604.15879
    Multilevel sparse kernel-based interpolation using conditionally positive definite radial basis functions. In A. Cangiani, R. Davidchack, E. H. Georgoulis, A. Gorban, J. Levesley, M. Tretyakov (eds.), ENUMATH '11 Proceedings, Leicester, Springer, 2013.

Other publications cited elsewhere:

  1. E. H. Georgoulis and E. Süli.
    hp-DGFEM on shape-irregular meshes: reaction-diffusion problems. Oxford University Computing Laboratory Technical Report 01/09 (2001).

  2. E. H. Georgoulis.
    Discontinuous Galerkin methods on shape-regular and anisotropic meshes. D.Phil. Thesis, Computing Laboratory, University of Oxford (2003).

  3. Z. Dong, E. H. Georgoulis, J. Levesley and F. Usta.
    Fast multilevel sparse Gaussian kernels for high-dimensional approximation and integration. PDF