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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.
}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/670.html} }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.