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

C. Bi & Y. Lin

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.

  • AMS Subject Headings

65N15, 65N30

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-9-999, author = {C. Bi and Y. Lin}, 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 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 -

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 and Y. Lin. (2012). Discontinuous Galerkin Method for Monotone Nonlinear Elliptic Problems. International Journal of Numerical Analysis and Modeling. 9 (4). 999-1024. doi:
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