14 citations · 18 across the 19 of their papers we have counts for
25 papers
Weighted regularity of fluid-structure interaction when the interface intersects the boundary
Zhaonan Dong, Tiantian Huang, Buyang Li
This paper analyzes the regularity of solutions to a fluid-structure interaction (FSI) problem involving a Stokesian fluid and a linear elastic solid in a two-dimensional polygonal…
Hypocoercivity-preserving space-time Galerkin methods for kinetic Fokker-Planck equations
Zhaonan Dong, Emmanuil H. Georgoulis
We design and analyse a family of hypocoercivity-preserving fully discrete Galerkin methods for the (inhomogeneous) kinetic Fokker--Planck (kFP) equations, a class of evolution PDE…
On -robust convergence and optimality of adaptive FEM driven by equilibrated-flux estimators
Théophile Chaumont-Frelet, Zhaonan Dong, Gregor Gantner +1
Building on existing -adaptive algorithms driven by equilibrated-flux estimators from [ESAIM Math. Model. Numer. Anal. 57 (2023), 329--366] and the references therein, we propo…
-reconstruction of piecewise polynomial fields with application to -a posteriori nonconforming error analysis for Maxwell's equations
Zhaonan Dong, Alexandre Ern
We devise and analyse a novel -reconstruction operator for piecewise polynomial fields on shape-regular simplicial meshes. The (non-polynomial) recon…
Asymptotic numerical hypocoercivity of the space-time discontinuous Galerkin method for the Kolmogorov equation
Zhaonan Dong, Emmanuil H. Georgoulis, Philip J. Herbert
We are concerned with discretisations of the classical Kolmogorov equation by a standard space-time discontinuous Galerkin method. {The} Kolmogorov equation serves as simple, yet r…
-error analysis of mixed-order hybrid high-order methods for elliptic problems on simplicial meshes
Zhaonan Dong, Alexandre Ern
We present both -a priori and -a posteriori error analysis of a mixed-order hybrid high-order (HHO) method to approximate second-order elliptic problems on simplicial meshe…
Homogeneous multigrid for hybrid discretizations: application to HHO methods
Daniele A. Di Pietro, Zhaonan Dong, Guido Kanschat +2
We prove the uniform convergence of the geometric multigrid V-cycle for hybrid high-order (HHO) and other discontinuous skeletal methods. Our results generalize previously establis…
A hypocoercivity-exploiting stabilised finite element method for Kolmogorov equation
Zhaonan Dong, Emmanuil H. Georgoulis, Philip J. Herbert
We propose a new stabilised finite element method for the classical Kolmogorov equation. The latter serves as a basic model problem for large classes of kinetic-type equations and,…
-optimal interior penalty discontinuous Galerkin methods for the biharmonic problem
Zhaonan Dong, Lorenzo Mascotto
We prove -optimal error estimates for interior penalty discontinuous Galerkin methods (IPDG) for the biharmonic problem with homogeneous essential boundary conditions. We consi…
An improved high-order method for elliptic multiscale problems
Zhaonan Dong, Moritz Hauck, Roland Maier
In this work, we propose a high-order multiscale method for an elliptic model problem with rough and possibly highly oscillatory coefficients. Convergence rates of higher order are…
A posteriori error estimates for discontinuous Galerkin methods on polygonal and polyhedral meshes
Andrea Cangiani, Zhaonan Dong, Emmanuil H. Georgoulis
We present a new residual-type energy-norm a posteriori error analysis for interior penalty discontinuous Galerkin (dG) methods for linear elliptic problems. The new error bounds a…
-hybrid high-order methods for biharmonic problems
Zhaonan Dong, Alexandre Ern
We devise and analyze -conforming hybrid high-order (HHO) methods to approximate biharmonic problems with either clamped or simply supported boundary conditions. -conform…
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…
Hybrid high-order method for singularly perturbed fourth-order problems on curved domains
Zhaonan Dong, Alexandre Ern
We propose a novel hybrid high-order method (HHO) to approximate singularly perturbed fourth-order PDEs on domains with a possibly curved boundary. The two key ideas in devising th…
Robust interior penalty discontinuous Galerkin methods
Zhaonan Dong, Emmanuil H. Georgoulis
Classical interior penalty discontinuous Galerkin (IPDG) methods for diffusion problems require a number of assumptions on the local variation of mesh-size, polynomial degree, and…
Hybrid high-order and weak Galerkin methods for the biharmonic problem
Zhaonan Dong, Alexandre Ern
We devise and analyze two hybrid high-order (HHO) methods for the numerical approximation of the biharmonic problem. The methods support polyhedral meshes, rely on the primal formu…
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…
-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…
Discontinuous Galerkin Methods for the Biharmonic Problem on Polygonal and Polyhedral Meshes
Zhaonan Dong
We introduce an -version symmetric interior penalty discontinuous Galerkin finite element method (DGFEM) for the numerical approximation of the biharmonic equation on general c…
Recovered finite element methods on polygonal and polyhedral meshes
Zhaonan Dong, Emmanuil H. Georgoulis, Tristan Pryer
Recovered finite element methods (R-FEM) have been recently introduced for meshes consisting of simplicial and/or box-type meshes. Here, utilising the flexibility of R-FEM framewor…
On the exponent of exponential convergence of the -version FEM spaces
Zhaonan Dong
We study the exponent of the exponential rate of convergence in terms of the number of degrees of freedom for various non-standard {-version} finite element spaces employing red…
Right orthogonal class of pure projective modules over pure hereditary rings
Umamaheswaran Arunachalam, Udhayakumar Ramalingam, Selvaraj Chelliah +1
We denote by the class of all pure projective modules. Present article we investigate -injective modules and these modules are defined via the vanishing…