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Hermitian green element solutions of the Burgers equation

✍ Scribed by Taigbenu, Akpofure E.

Publisher: John Wiley and Sons
Year: 1999
Tongue: English
Weight: 108 KB
Volume: 15
Category: Article
ISSN: 1069-8299
DOI: 10.1002/(sici)1099-0887(199909)15:9<611::aid-cnm229>3.0.co;2-6

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✦ Synopsis

Our earlier paper incorporated linear basis functions for the representation of the distribution of the primary variable (velocity) into a model of the Green element method (GEM) for the solution of Burgers' equation. GEM is an element-by-element numerical procedure of implementing the singular boundary integral theory which yields a banded coecient matrix that is easier to decompose, thereby enhancing computational eciency. The performance of that earlier model depended partly on how well the velocity was represented. For shock propagation problems in which large gradients of the velocity are encountered, the use of linear interpolation functions may be inadequate. Here, we incorporate the cubic Hermitian interpolation functions into that same model, and demonstrate that the accuracy of the numerical solution of Burgers' equation is enhanced, but at a higher computing cost.

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