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Volume 19, Issue 2-3
On an Adaptive LDG for the $P$-Laplace Problem

Dongjie Liu, Le Zhou & Xiaoping Zhang

Int. J. Numer. Anal. Mod., 19 (2022), pp. 315-328.

Published online: 2022-04

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  • Abstract

In this paper we consider the adaptive local discontinuous Galerkin(LDG) method for the $p$-Laplace problem in polygonal regions in $\mathbb{R}^2$. We present new sharper a posteriori error estimate for the LDG approximation of the $p$-Laplacian in the new framework. Several examples are given to confirm the reliability of the estimate.

  • Keywords

$p$-Laplace, local discontinuous Galerkin methods, quasi-norm, a posteriori error estimate.

  • AMS Subject Headings

65N15, 65N30

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-19-315, author = {Liu , DongjieZhou , Le and Zhang , Xiaoping}, title = {On an Adaptive LDG for the $P$-Laplace Problem }, journal = {International Journal of Numerical Analysis and Modeling}, year = {2022}, volume = {19}, number = {2-3}, pages = {315--328}, abstract = {

In this paper we consider the adaptive local discontinuous Galerkin(LDG) method for the $p$-Laplace problem in polygonal regions in $\mathbb{R}^2$. We present new sharper a posteriori error estimate for the LDG approximation of the $p$-Laplacian in the new framework. Several examples are given to confirm the reliability of the estimate.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/20483.html} }
TY - JOUR T1 - On an Adaptive LDG for the $P$-Laplace Problem AU - Liu , Dongjie AU - Zhou , Le AU - Zhang , Xiaoping JO - International Journal of Numerical Analysis and Modeling VL - 2-3 SP - 315 EP - 328 PY - 2022 DA - 2022/04 SN - 19 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/20483.html KW - $p$-Laplace, local discontinuous Galerkin methods, quasi-norm, a posteriori error estimate. AB -

In this paper we consider the adaptive local discontinuous Galerkin(LDG) method for the $p$-Laplace problem in polygonal regions in $\mathbb{R}^2$. We present new sharper a posteriori error estimate for the LDG approximation of the $p$-Laplacian in the new framework. Several examples are given to confirm the reliability of the estimate.

Dongjie Liu, Le Zhou & Xiaoping Zhang. (2022). On an Adaptive LDG for the $P$-Laplace Problem . International Journal of Numerical Analysis and Modeling. 19 (2-3). 315-328. doi:
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