3 papers
math.NA2020
Adaptive non-hierarchical Galerkin methods for parabolic problems with application to moving mesh and virtual element methods
Andrea Cangiani, Emmanuil H. Georgoulis, Oliver J. Sutton
We present a posteriori error estimates for inconsistent and non-hierarchical Galerkin methods for linear parabolic problems, allowing them to be used in conjunction with very gene…
math.NA2019
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…
math.NA2019
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…