TY - JOUR
T1 - Energy Norm Error Estimates for Averaged Discontinuous Galerkin Methods in 1 Dimension
AU - G. Csorgo & F. Izsak
JO - International Journal of Numerical Analysis and Modeling
VL - 3
SP - 567
EP - 586
PY - 2014
DA - 2014/11
SN - 11
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/542.html
KW - discontinuous Galerkin method, smoothing technique, and error estimation.
AB - <p style="text-align: justify;">Numerical solution of one-dimensional elliptic problems is investigated using an averaged discontinuous discretization. The corresponding numerical method can be performed using
the favorable properties of the discontinuous Galerkin (dG) approach, while for the average an
error estimation is obtained in the $H^1$-seminorm. We point out that this average can be regarded
as a lower order modification of the average of a well-known overpenalized symmetric interior
penalty (IP) method. This allows a natural derivation of the overpenalized IP methods.</p>