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Convergence of a Galerkin method for 2-D discontinuous Euler flows

โœ Scribed by Jian-Guo Liu; Zhouping Xin

Publisher
John Wiley and Sons
Year
2000
Tongue
English
Weight
75 KB
Volume
53
Category
Article
ISSN
0010-3640

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โœฆ Synopsis

We prove the convergence of a discontinuous Galerkin method approximating the 2-D incompressible Euler equations with discontinuous initial vorticity: ฯ‰ 0 โˆˆ L 2 (โ„ฆ). Furthermore, when ฯ‰ 0 โˆˆ L โˆž (โ„ฆ), the whole sequence is shown to be strongly convergent. This is the first convergence result in numerical approximations of this general class of discontinuous flows. Some important flows such as vortex patches belong to this class.

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