TY - JOUR
T1 - A New $a$ $Posteriori$ Error Estimate for the Interior Penalty Discontinuous Galerkin Method
AU - Yang , Wei
AU - Cao , Luling
AU - Huang , Yunqing
AU - Cui , Jintao
JO - International Journal of Numerical Analysis and Modeling
VL - 2
SP - 210
EP - 224
PY - 2018
DA - 2018/10
SN - 16
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/12800.html
KW - Interior penalty discontinuous Galerkin method, a posteriori error estimate, adaptive finite element methods, Gauss-Seidel iterative method.
AB - <p style="text-align: justify;">In this paper, we develop the adaptive interior penalty discontinuous Galerkin method
based on a new $a$ $posteriori$ error estimate for the second-order elliptic boundary-value problems.
The new $a$ $posteriori$ error estimate is motivated from the smoothing iteration of the $m$-time
Gauss-Seidel iterative method, and it is used to construct the adaptive finite element method.
The efficiency and robustness of the proposed adaptive method is demonstrated by extensive
numerical experiments.</p>