# Paper on a Non-dissipative space–time hp-discontinuous Galerkin method for the time-dependent Maxwell equations published in JCP

Our paper dealing with the PhD project of Martin Lilienthal has been published in JCP: Non-dissipative space–time hp-discontinuous Galerkin method for the time-dependent Maxwell equations. The abstract reads:

A finite element method for the solution of the time-dependent Maxwell equations in mixed form is presented. The method allows for local hp-refinement in space and in time. To this end, a space–time Galerkin approach is employed. In contrast to the space–time DG method introduced in [Van der Vegt, JCP(182) 2002] test and trial spaces do not coincide. This allows for obtaining a non-dissipative method. To obtain an efficient implementation, a hierarchical tensor product basis in space and time is proposed. This allows to evaluate the local residual with a complexity of $$\mathcal{O}(p^4)$$ and $$\mathcal{O}(p^5)$$ for affine and non-affine elements, respectively.

# Paper on a Non-dissipative space-time hp-discontinuous Galerkin method for the time-dependent Maxwell Equations

Martin Lilienthal developed a space-time discontinuous Galerkin method. Unlike other works, this formulation is non-dissipative, which is achieved through non-coinciding choices of the trial and test spaces. Please find the preprint on arXiv.

# DFG granted project prolongation

The German Research Foundation DFG (Deutsche Forschungsgemeinschaft) positively evaluated the prolongation proposal for Martin Lilienthal‘s PhD project Autonome Steuerung von Gitteradaptionen im Rahmen der Diskontinuierlichen Galerkin Methode angewandt auf Probleme der Elektrodynamik (Autonomous Control of Mesh Adaptations for the Discontinuous Galerkin Method Applied to Problems in Electrodynamics).

# CEM Group at the ECMI Conference

Martin Lilienthal will attend the 17th European Conference on Mathematics for Industry (ECMI) to be held July 23-27 2012 at Lund, Sweden. He will contribute with his talk on a

Non-dissipative space time hp-discontinuous Galerkin method for the time-dependent Maxwell equations

to the mini-symposium organized by Mike Botchev and Wil Schilders.