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.
Yesterday Cui Jian successfully defended his PhD thesis with the title
Body-Fitting Meshes for the Discontinuous Galerkin Method.
The slides of today’s lecture on the Discontinuous Galerkin Method are available here (25 MB).
If you are interested in a project work or look for a bachelor/master thesis send me an email or come by.
Fritz Kretzschmar, Igor Tsukerman and started working on a novel DG method using a Trefftz-type basis in time-domain. The method is formulated in a space-time FE setting and provides high order approximations in both, space and time, where the high order accuracy in time comes at no extra costs in terms in degrees of freedom. We demonstrated spectral convergence over the full space-time domain.
You can get the preprint on arXiv.