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An HDG method with orthogonal projections in facet integrals. (arXiv:1711.05396v1 [math.NA])
来源于:arXiv
We propose and analyze a new hybridizable discontinuous Galerkin (HDG) method
for second-order elliptic problems. Our method is obtained by inserting the
$L^2$-orthogonal projection onto the approximate space for a numerical trace
into all facet integrals in the usual HDG formulation. The orders of
convergence for all variables are optimal if we use polynomials of degree
$k+l$, $k+1$ and $k$, where $k$ and $l$ are any non-negative integers, to
approximate the vector, scalar and trace variables, which implies that our
method can achieve superconvergence for the scalar variable without
postprocessing. Numerical results are presented to verify the theoretical
results. 查看全文>>