Year: 2011
Journal of Computational Mathematics, Vol. 29 (2011), Iss. 5 : pp. 491–500
Abstract
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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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.1105-m3392
Journal of Computational Mathematics, Vol. 29 (2011), Iss. 5 : pp. 491–500
Published online: 2011-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 10
Keywords: Adaptive finite element Nonlinear hyperbolic conservation law.
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