Abstract
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 Ie{cyrillic, ukrainian} H1 (Ω). 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.
Original language | English |
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Pages (from-to) | 991024 |
Number of pages | 1 |
Journal | International Journal of Numerical Analysis and Modeling |
Volume | 9 |
Issue number | 4 |
Publication status | Published - 29 Jun 2012 |
Keywords
- A posteriori error estimate
- A priori error estimate
- Discontinuous Galerkin method
- Monotone
- Nonlinear elliptic problems
ASJC Scopus subject areas
- Numerical Analysis