Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Arbitrary high order accurate space-time discontinuous Galerkin finite
  element schemes on staggered unstructured meshes for linear elasticity   In this paper we propose a new high order accurate space-time DG finite
element scheme for the solution of the linear elastic wave equations in first
order velocity-stress formulation in two and three-space dimensions on
staggered unstructured triangular and tetrahedral meshes. The method reaches
arbitrary high order of accuracy in both space and time via the use of
space-time basis and test functions. Within the staggered mesh formulation, we
define the discrete velocity field in the control volumes of a primary mesh,
while the discrete stress tensor is defined on a face-based staggered dual
mesh. The space-time DG formulation leads to an implicit scheme that requires
the solution of a linear system for the unknown degrees of freedom at the new
time level. The number of unknowns is reduced at the aid of the Schur
complement, so that in the end only a linear system for the degrees of freedom
of the velocity field needs to be solved. Thanks to the use of a spatially
staggered mesh, the stencil of the final velocity system involves only the
element and its direct neighbors. The resulting linear system can be
efficiently solved via matrix-free iterative methods. The chosen discretization
and the linear nature of the governing PDE system lead to an unconditionally
stable scheme, which allows large time steps even for low quality meshes that
contain sliver elements. The fully discrete staggered space-time DG method is
proven to be energy stable for any order of accuracy, for any mesh and for any
time step size. For the particular case of Crank-Nicolson time discretization
and homogeneous material, the final velocity system can be proven to be
symmetric and positive definite and in this case the scheme is also exactly
energy preserving. The new scheme is applied to several test problems in two
and three space dimensions, providing also a comparison with high order
explicit ADER-DG schemes

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The categories of this paper are: hep-ex
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The categories of this paper are: nucl-th
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The categories of this paper are: q-bio
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The categories of this paper are: gr-qc
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The categories of this paper are: cond-mat
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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: atom-ph
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The categories of this paper are: physics
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The categories of this paper are: funct-an
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The categories of this paper are: adap-org
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The categories of this paper are: q-alg
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The categories of this paper are: math-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-ph
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The categories of this paper are: econ