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An Optimal Embedded Discontinuous Galerkin Method for Second-Order Elliptic Problems. (arXiv:1711.05544v1 [math.NA])
来源于:arXiv
The embedded discontinuous Galerkin (EDG) method by Cockburn et al. [SIAM J.
Numer. Anal., 2009, 47(4), 2686-2707] is obtained from the hybridizable
discontinuous Galerkin method by changing the space of the Lagrangian
multiplier from discontinuous functions to continuous ones, and adopts
piecewise polynomials of equal degrees on simplex meshes for all variables. In
this paper, we analyze a new EDG method for second order elliptic problems on
polygonal/polyhedral meshes. By using piecewise polynomials of degrees $k+1$,
$k+1$, $k$ ($k\geq 0$) to approximate the potential, numerical trace and flux,
respectively, the new method is shown to yield optimal convergence rates for
both the potential and flux approximations. Numerical experiments are provided
to confirm the theoretical results. 查看全文>>