69 citations · 229 across the 40 of their papers we have counts for
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Convergence of adaptive discontinuous Galerkin methods (corrected version of [Math. Comp. 87 (2018), no. 314, 2611--2640])
Christian Kreuzer, Emmanuil H. Georgoulis
We develop a general convergence theory for adaptive discontinuous Galerkin methods for elliptic PDEs covering the popular SIPG, NIPG and LDG schemes as well as all practically rel…
A posteriori error estimates for the Allen-Cahn problem
Konstantinos Chrysafinos, Emmanuil H. Georgoulis, Dimitra Plaka
This work is concerned with the proof of \emph{a posteriori} error estimates for fully-discrete Galerkin approximations of the Allen-Cahn equation in two and three spatial dimensio…
-Version discontinuous Galerkin methods on essentially arbitrarily-shaped elements
Andrea Cangiani, Zhaonan Dong, Emmanuil H. Georgoulis
We extend the applicability of the popular interior-penalty discontinuous Galerkin (dG) method discretizing advection-diffusion-reaction problems to meshes comprising extremely gen…