@Article{JCM-29-491,
author = {Zhengfu Xu, Jinchao Xu, and Chi-Wang Shu},
title = {A High Order Adaptive Finite Element Method for Solving Nonlinear Hyperbolic Conservation Laws},
journal = {Journal of Computational Mathematics},
year = {2011},
volume = {29},
number = {5},
pages = {491--500},
abstract = {<p style="text-align: justify;">In this note, we apply the $h$-adaptive streamline diffusion finite element method with a small mesh-dependent artificial viscosity to solve nonlinear hyperbolic partial differential equations, with the objective of achieving high order accuracy and mesh efficiency. We compute the numerical solution to a steady state Burgers equation and the solution to a converging-diverging nozzle problem. The computational results verify that, by suitably choosing the artificial viscosity coefficient and applying the adaptive strategy based on a posterior error estimate by Johnson et al., an order of $N^{-3/2}$ accuracy can be obtained when continuous piecewise linear elements are used, where $N$ is the number of elements.</p>},
issn = {1991-7139},
doi = {https://doi.org/10.4208/jcm.1105-m3392},
url = {http://global-sci.org/intro/article_detail/jcm/8490.html}
}