TY - JOUR
T1 - Discontinuous Galerkin Method for Monotone Nonlinear Elliptic Problems
AU - C. Bi & Y. Lin
JO - International Journal of Numerical Analysis and Modeling
VL - 4
SP - 999
EP - 1024
PY - 2012
DA - 2012/09
SN - 9
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/670.html
KW - discontinuous Galerkin method, nonlinear elliptic problems, monotone, a priori error estimate, a posteriori error estimate.
AB - <p style="text-align: justify;">In this paper, we consider the incomplete interior penalty method for a class of second
order monotone nonlinear elliptic problems. Using the theory of monotone operators, we show
that the corresponding discrete method has a unique solution. The a priori error estimate in an
energy norm is developed under the minimal regularity assumption on the exact solution, i.e., $u \in H^1(\Omega)$. Moreover, we propose a residual-based a posteriori error estimator and derive the
computable upper and lower bounds on the error in an energy norm.</p>