2381/39473 Andrea Cangiani Andrea Cangiani Zhaonan Dong Zhaonan Dong Emmanuil H. Georgoulis Emmanuil H. Georgoulis $hp$-Version space-time discontinuous Galerkin methods for parabolic problems on prismatic meshes University of Leicester 2017 space-time discontinuous Galerkin hp–finite element methods reduced cardinality basis functions discontinuous Galerkin time-stepping 2017-03-15 16:01:58 Journal contribution https://figshare.le.ac.uk/articles/journal_contribution/_hp_-Version_space-time_discontinuous_Galerkin_methods_for_parabolic_problems_on_prismatic_meshes/10235627 We present a new hp-version space-time discontinuous Galerkin (dG) finite element method for the numerical approximation of parabolic evolution equations on general spatial meshes consisting of polygonal/polyhedral (polytopic) elements, giving rise to prismatic space-time elements. A key feature of the proposed method is the use of space-time elemental polynomial bases of total degree, say p, defined in the physical coordinate system, as opposed to standard dG-time-stepping methods whereby spatial elemental bases are tensorized with temporal basis functions. This approach leads to a fully discrete hp-dG scheme using fewer degrees of freedom for each time step, compared to dG time-stepping schemes employing tensorized space-time basis, with acceptable deterioration of the approximation properties. A second key feature of the new space-time dG method is the incorporation of very general spatial meshes consisting of possibly polygonal/polyhedral elements with arbitrary number of faces. A priori error bounds are shown for the proposed method in various norms. An extensive comparison among the new space-time dG method, the (standard) tensorized space-time dG methods, the classical dG-time-stepping, and conforming finite element method in space, is presented in a series of numerical experiments.