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

Zhengfu Xu, Jinchao Xu, Chi Wang Shu

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)491-500
Number of pages10
JournalJournal of Computational Mathematics
Volume29
Issue number5
DOIs
StatePublished - Sep 2011

All Science Journal Classification (ASJC) codes

  • Computational Mathematics

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