11 papers
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…
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…
A posteriori error analysis and adaptivity of a space-time finite element method for the wave equation in second order formulation
Zhaonan Dong, Emmanuil H. Georgoulis, Lorenzo Mascotto +1
We establish rigorous \emph{a posteriori} error bounds for a space-time finite element method of arbitrary order discretising linear wave problems in second order formulation. The…
-Version robust interior penalty discontinuous Galerkin methods for the -Laplacian on simplicial and on essentially arbitrarily-shaped element meshes
Emmanuil H. Georgoulis, Panagiotis Paraschis
We consider the discretization of the -Laplacian equation with an interior penalty discontinuous Galerkin method. We prove novel trace-type inverse estimates, leading to uncondi…
Space-time finite element methods for nonlinear wave equations via elliptic regularisation
Lehel Banjai, Emmanuil H. Georgoulis, Brian Hennessy
We present and analyse a new conforming space-time Galerkin discretisation of a semi-linear wave equation, based on a variational formulation derived from De Giorgi's elliptic regu…
A nodally bound-preserving composite discontinuous Galerkin method on polytopic meshes
Abdolreza Amiri, Gabriel R. Barrenechea, Emmanuil H. Georgoulis +1
We introduce a nodally bound-preserving Galerkin method for second-order elliptic problems on general polygonal/polyhedral, henceforth collectively termed as \emph{polytopic}, mesh…