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.