hp-version discontinuous Galerkin methods on polygonal and polyhedral meshes
A Cangiani, EH Georgoulis… - Mathematical Models and …, 2014 - World Scientific
An hp-version interior penalty discontinuous Galerkin method (DGFEM) for the numerical
solution of second-order elliptic partial differential equations on general computational …
solution of second-order elliptic partial differential equations on general computational …
Review of discontinuous Galerkin finite element methods for partial differential equations on complicated domains
The numerical approximation of partial differential equations (PDEs) posed on complicated
geometries, which include a large number of small geometrical features or microstructures …
geometries, which include a large number of small geometrical features or microstructures …
Adaptive discontinuous Galerkin methods for elliptic interface problems
An interior-penalty discontinuous Galerkin (dG) method for an\penalty-10000 elliptic
interface problem involving, possibly, curved interfaces, with flux-\penalty-10000 balancing …
interface problem involving, possibly, curved interfaces, with flux-\penalty-10000 balancing …
hp-version discontinuous Galerkin methods for advection-diffusion-reaction problems on polytopic meshes
We consider the hp-version interior penalty discontinuous Galerkin finite element method
(DGFEM) for the numerical approximation of the advection-diffusion-reaction equation on …
(DGFEM) for the numerical approximation of the advection-diffusion-reaction equation on …
A high-order discontinuous Galerkin method for nonlinear sound waves
We propose a high-order discontinuous Galerkin scheme for nonlinear acoustic waves on
polytopic meshes. To model sound propagation with losses through homogeneous media …
polytopic meshes. To model sound propagation with losses through homogeneous media …
A high-order approach to elliptic multiscale problems with general unstructured coefficients
R Maier - SIAM Journal on Numerical Analysis, 2021 - SIAM
We propose a multiscale approach for an elliptic multiscale setting with general unstructured
diffusion coefficients that is able to achieve high-order convergence rates with respect to the …
diffusion coefficients that is able to achieve high-order convergence rates with respect to the …
hp analysis of a hybrid DG method for Stokes flow
This manuscript deals with the hp error analysis of a hybrid discontinuous Galerkin method
for incompressible flow. Besides the usual coercivity and boundedness estimates, we …
for incompressible flow. Besides the usual coercivity and boundedness estimates, we …
Multigrid algorithms for hp hp-version interior penalty discontinuous Galerkin methods on polygonal and polyhedral meshes
In this paper we analyze the convergence properties of two-level and W-cycle multigrid
solvers for the numerical solution of the linear system of equations arising from hp-version …
solvers for the numerical solution of the linear system of equations arising from hp-version …
[HTML][HTML] Exponential convergence of the hp virtual element method in presence of corner singularities
In the present work, we analyze the hp version of virtual element methods for the 2D Poisson
problem. We prove exponential convergence of the energy error employing sequences of …
problem. We prove exponential convergence of the energy error employing sequences of …
ℎ𝑝-version discontinuous Galerkin methods on essentially arbitrarily-shaped elements
We extend the applicability of the popular interior penalty discontinuous Galerkin method
discretizing advection-diffusion-reaction problems to meshes comprising extremely general …
discretizing advection-diffusion-reaction problems to meshes comprising extremely general …