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

Jian-Guo Liu jliu@math.umd.edu ZHOUPING XIN The Chinese University of Hong Kong

Numerical Analysis and Scientific Computing mathscidoc:1702.25061

Communications on Pure and Applied Mathematics, 53, (6), 2000.3
We prove the convergence of a discontinuous Galerkin method approximating the 2-D incompressible Euler equations with discontinuous initial vorticity:$omega_0 in L^2(Omega)$. Furthermore, when $omega_0 in L^infty(Omega)$, 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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@inproceedings{jian-guo2000convergence,
  title={Convergence of a Galerkin method for 2-D discontinuous Euler flows},
  author={Jian-Guo Liu, and ZHOUPING XIN},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170209124325805616392},
  booktitle={Communications on Pure and Applied Mathematics},
  volume={53},
  number={6},
  year={2000},
}
Jian-Guo Liu, and ZHOUPING XIN. Convergence of a Galerkin method for 2-D discontinuous Euler flows. 2000. Vol. 53. In Communications on Pure and Applied Mathematics. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170209124325805616392.
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