I am a Professor of Mathematics (p/t) and I also hold an appointment as Professor at the National Technical University of Athens.
Numerical Analysis. In particular:
a) Computational Methods for Partial Differential Equations arising in solids, fluids, mathematical biology and multiscale problems; in particular, finite element methods, discontinuous Galerkin methods, finite volume methods, multiscale methods, their error analysis and adaptivity strategies.
b) Approximation Theory; in particular, multivariate approximation using polynomials, radial basis functions and hierarchical/wavelet bases, high-dimensional approximation.
(0) 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).
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),
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).
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).
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).
A. Cangiani, E. H. Georgoulis and P. Houston.
Version discontinuous Galerkin methods on polygonal and polyhedral meshes. Mathematical Models and Methods in Applied Sciences 24(10) pp. 2009 (2014).
Numerical Analysis of PDEs.
Computational Methods for PDEs with Finite Elements. Computational Methods for PDEs with Applications.
Press and media