Volume 9, Issue 4
Discontinuous Galerkin Method for Monotone Nonlinear Elliptic Problems

Int. J. Numer. Anal. Mod., 9 (2012), pp. 999-1024.

Published online: 2012-09

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• 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., $u \in H^1(\Omega)$. 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.

• Keywords

discontinuous Galerkin method, nonlinear elliptic problems, monotone, a priori error estimate, a posteriori error estimate.

65N15, 65N30

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@Article{IJNAM-9-999, author = {}, title = {Discontinuous Galerkin Method for Monotone Nonlinear Elliptic Problems}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2012}, volume = {9}, number = {4}, pages = {999--1024}, 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., $u \in H^1(\Omega)$. 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} }
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.

C. Bi & Y. Lin. (1970). Discontinuous Galerkin Method for Monotone Nonlinear Elliptic Problems. International Journal of Numerical Analysis and Modeling. 9 (4). 999-1024. doi:
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