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
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).
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).
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
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
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
E. H.
Georgoulis and C. G. Makridakis. Lower bounds, elliptic reconstruction, and a posteriori error control
of parabolic problems.IMA
Journal of Numerical Analysis, accepted for publication.
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.
G. R.
Barrenechea, E. H. Georgoulis, T. Pryer and A. Veeser. A nodally bound-preserving finite element method. Submitted for
publication.
A.
Cangiani, Z. Dong, and E. H. Georgoulis. A posteriori error estimates for discontinuous Galerkin methods on
polygonal and polyhedral meshes. Submitted for publication. PDF
Contributions in conference
proceedings:
E. H.
Georgoulis and D. Loghin. Krylov-Subspace preconditioners
for discontinuous Galerkin finite element methods. ECCOMAS CFD 2006
Proceedings.
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.
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.
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.
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.
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.
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.
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.
E. H.
Georgoulis, J. Levesley and F. Subhan. 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:
E. H.
Georgoulis and E. Süli. hp--DGFEM on shape-irregular meshes: reaction-diffusion problems.
Oxford University Computing Laboratory Technical Report 01/09 (2001).
E. H.
Georgoulis. Discontinuous Galerkin methods on shape-regular and anisotropic meshes.
D.Phil. Thesis, Computing Laboratory, University of Oxford (2003).
Z. Dong,
E. H. Georgoulis, J. Levesley and F. Usta. Fast multilevel sparse Gaussian kernels for high-dimensional approximation
and integration. PDF