@Article{CiCP-9-2,
author = {},
title = {A Compact High Order Space-Time Method for Conservation Laws},
journal = {Communications in Computational Physics},
year = {2011},
volume = {9},
number = {2},
pages = {441--480},
abstract = {<p style="text-align: justify;">This paper presents a novel high-order space-time method for hyperbolic
conservation laws. Two important concepts, the staggered space-time mesh of the
space-time conservation element/solution element (CE/SE) method and the local discontinuous
basis functions of the space-time discontinuous Galerkin (DG) finite element
method, are the two key ingredients of the new scheme. The staggered space-time
mesh is constructed using the cell-vertex structure of the underlying spatial mesh.
The universal definitions of CEs and SEs are independent of the underlying spatial
mesh and thus suitable for arbitrarily unstructured meshes. The solution within each
physical time step is updated alternately at the cell level and the vertex level. For
this solution updating strategy and the DG ingredient, the new scheme here is termed
as the discontinuous Galerkin cell-vertex scheme (DG-CVS). The high order of accuracy
is achieved by employing high-order Taylor polynomials as the basis functions
inside each SE. The present DG-CVS exhibits many advantageous features such as
Riemann-solver-free, high-order accuracy, point-implicitness, compactness, and ease
of handling boundary conditions. Several numerical tests including the scalar advection
equations and compressible Euler equations will demonstrate the performance of
the new method.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.050309.110510a},
url = {https://global-sci.com/article/80854/a-compact-high-order-space-time-method-for-conservation-laws}
}