TY - JOUR

T1 - A high order adaptive finite element method for solving nonlinear hyperbolic conservation laws

AU - Xu, Zhengfu

AU - Xu, Jinchao

AU - Shu, Chi Wang

PY - 2011/9

Y1 - 2011/9

N2 - 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.

AB - 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.

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U2 - 10.4208/jcm.1105-m3392

DO - 10.4208/jcm.1105-m3392

M3 - Article

AN - SCOPUS:80555127200

SN - 0254-9409

VL - 29

SP - 491

EP - 500

JO - Journal of Computational Mathematics

JF - Journal of Computational Mathematics

IS - 5

ER -