TY - JOUR
T1 - A High Order Adaptive Finite Element Method for Solving Nonlinear Hyperbolic Conservation Laws
AU - Zhengfu Xu, Jinchao Xu, & Chi-Wang Shu
JO - Journal of Computational Mathematics
VL - 5
SP - 491
EP - 500
PY - 2011
DA - 2011/10
SN - 29
DO - http://doi.org/10.4208/jcm.1105-m3392
UR - https://global-sci.org/intro/article_detail/jcm/8490.html
KW - Adaptive finite element, Nonlinear hyperbolic conservation law.
AB - <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>