@Article{CiCP-8-3,
author = {},
title = {The Direct Discontinuous Galerkin (DDG) Method for Diffusion with Interface Corrections},
journal = {Communications in Computational Physics},
year = {2010},
volume = {8},
number = {3},
pages = {541--564},
abstract = {<p style="text-align: justify;">Based on a novel numerical flux involving jumps of even order derivatives
of the numerical solution, a direct discontinuous Galerkin (DDG) method for diffusion
problems was introduced in [H. Liu and J. Yan, SIAM J. Numer. Anal. 47(1) (2009),
475-698]. In this work, we show that higher order (k≥4) derivatives in the numerical
flux can be avoided if some interface corrections are included in the weak formulation
of the DDG method; still the jump of 2nd order derivatives is shown to be important
for the method to be efficient with a fixed penalty parameter for all p<sup>k&nbsp;</sup>elements. The
refined DDG method with such numerical fluxes enjoys the optimal (k+1)th order
of accuracy. The developed method is also extended to solve convection diffusion
problems in both one- and two-dimensional settings. A series of numerical tests are
presented to demonstrate the high order accuracy of the method.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.010909.011209a},
url = {https://global-sci.com/article/81041/the-direct-discontinuous-galerkin-ddg-method-for-diffusion-with-interface-corrections}
}