@Article{CiCP-6-1,
author = {},
title = {A Family of Characteristic Discontinuous Galerkin Methods for Transient Advection-Diffusion Equations and Their Optimal-Order L<sup>2</sup> Error Estimates},
journal = {Communications in Computational Physics},
year = {2009},
volume = {6},
number = {1},
pages = {203--230},
abstract = {<p style="text-align: justify;">We develop a family of characteristic discontinuous Galerkin methods for
transient advection-diffusion equations, including the characteristic NIPG, OBB, IIPG,
and SIPG schemes. The derived schemes possess combined advantages of Eulerian-Lagrangian
methods and discontinuous Galerkin methods. An optimal-order error
estimate in the L<sup>2</sup> norm and a superconvergence estimate in a weighted energy norm
are proved for the characteristic NIPG, IIPG, and SIPG scheme. Numerical experiments
are presented to confirm the optimal-order spatial and temporal convergence
rates of these schemes as proved in the theorems and to show that these schemes compare
favorably to the standard NIPG, OBB, IIPG, and SIPG schemes in the context of
advection-diffusion equations.</p>},
issn = {1991-7120},
doi = {https://doi.org/2009-CiCP-7030},
url = {https://global-sci.com/article/81132/a-family-of-characteristic-discontinuous-galerkin-methods-for-transient-advection-diffusion-equations-and-their-optimal-order-lsup2sup-error-estimates}
}