4 papers
Local decay rates of best-approximation errors using vector-valued finite elements for fields with low regularity and integrable curl or divergence
Zhaonan Dong, Alexandre Ern, Jean-Luc Guermond
We estimate best-approximation errors using vector-valued finite elements for fields with low regularity in the scale of fractional-order Sobolev spaces. By assuming additionally t…
On the suboptimality of the p-version discontinuous Galerkin methods for first order hyperbolic problems
Zhaonan Dong, Lorenzo Mascotto
We address the issue of the suboptimality in the p-version discontinuous Galerkin (dG) methods for first order hyperbolic problems. The convergence rate is derived for the upwind d…
Residual-based a posteriori error estimates for -discontinuous Galerkin discretisations of the biharmonic problem
Zhaonan Dong, Lorenzo Mascotto, Oliver J. Sutton
We introduce a residual-based a posteriori error estimator for a novel -version interior penalty discontinuous Galerkin method for the biharmonic problem in two and three dimen…
GPU-accelerated discontinuous Galerkin methods on polytopic meshes
Zhaonan Dong, Emmanuil H. Georgoulis, Thomas Kappas
Discontinuous Galerkin (dG) methods on meshes consisting of polygonal/polyhedral (henceforth, collectively termed as \emph{polytopic}) elements have received considerable attention…