On the Convergence of the Spectral Viscosity Method for the Two-Dimensional Incompressible Euler Equations with Rough Initial Data
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Date
2020-10Type
- Journal Article
Abstract
We propose a spectral viscosity method to approximate the two-dimensional Euler equations with rough initial data and prove that the method converges to a weak solution for a large class of initial data, including when the initial vorticity is in the so-called Delort class, i.e., it is a sum of a signed measure and an integrable function. This provides the first convergence proof for a numerical method approximating the Euler equations with such rough initial data and closes the gap between the available existence theory and rigorous convergence results for numerical methods. We also present numerical experiments, including computations of vortex sheets and confined eddies, to illustrate the proposed method. Show more
Publication status
publishedExternal links
Journal / series
Foundations of Computational MathematicsVolume
Pages / Article No.
Publisher
SpringerSubject
Incompressible Euler; Spectral viscosity; Vortex sheet; Convergence; Compensated compactnessOrganisational unit
03851 - Mishra, Siddhartha / Mishra, Siddhartha
Funding
770880 - Computation and analysis of statistical solutions of fluid flow (EC)
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Is new version of: http://hdl.handle.net/20.500.11850/364556
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