9 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…
-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…
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…
-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…
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…