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Convergence of a Galerkin method for 2‐D discontinuous Euler flows
Author(s) -
Liu JianGuo,
Xin Zhouping
Publication year - 2000
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/(sici)1097-0312(200006)53:6<786::aid-cpa3>3.0.co;2-y
Subject(s) - mathematics , discontinuous galerkin method , convergence (economics) , vorticity , euler equations , euler's formula , sequence (biology) , mathematical analysis , compressibility , vortex , galerkin method , backward euler method , flow (mathematics) , class (philosophy) , geometry , finite element method , physics , mechanics , computer science , genetics , artificial intelligence , biology , economics , thermodynamics , economic growth
We prove the convergence of a discontinuous Galerkin method approximating the 2‐D incompressible Euler equations with discontinuous initial vorticity: ω 0 ϵ L 2 (Ω). Furthermore, when ω 0 ϵ L ∞ (Ω), 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. © 2000 John Wiley & Sons, Inc.