TY - JOUR T1 - Discontinuous Galerkin Method for Monotone Nonlinear Elliptic Problems 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 -

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.