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

Publication ,  Journal Article
Liu, JG; Xin, Z
Published in: Communications on Pure and Applied Mathematics
January 1, 2000
Published version (DOI)

We prove the convergence of a discontinuous Galerkin method approximating the 2-D incompressible Euler equations with discontinuous initial vorticity: ω0 ∈ L2(Ω). Furthermore, when ω0 ∈ 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.

Duke Scholars

Jian-Guo Liu
Author Jian-Guo Liu Physics

Published In

Communications on Pure and Applied Mathematics

DOI

10.1002/(SICI)1097-0312(200006)53:6<786::AID-CPA3>3.0.CO;2-Y

ISSN

0010-3640

Publication Date

January 1, 2000

Volume

53

Issue

6

Start / End Page

786 / 798

Related Subject Headings

  • General Mathematics
  • 4904 Pure mathematics
  • 4901 Applied mathematics
 

Citation

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ICMJE
MLA
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Liu, J. G., & Xin, Z. (2000). Convergence of a Galerkin method for 2-D discontinuous Euler flows. Communications on Pure and Applied Mathematics, 53(6), 786–798. https://doi.org/10.1002/(SICI)1097-0312(200006)53:6<786::AID-CPA3>3.0.CO;2-Y
Liu, J. G., and Z. Xin. “Convergence of a Galerkin method for 2-D discontinuous Euler flows.” Communications on Pure and Applied Mathematics 53, no. 6 (January 1, 2000): 786–98. https://doi.org/10.1002/(SICI)1097-0312(200006)53:6<786::AID-CPA3>3.0.CO;2-Y.
Liu JG, Xin Z. Convergence of a Galerkin method for 2-D discontinuous Euler flows. Communications on Pure and Applied Mathematics. 2000 Jan 1;53(6):786–98.
Liu, J. G., and Z. Xin. “Convergence of a Galerkin method for 2-D discontinuous Euler flows.” Communications on Pure and Applied Mathematics, vol. 53, no. 6, Jan. 2000, pp. 786–98. Scopus, doi:10.1002/(SICI)1097-0312(200006)53:6<786::AID-CPA3>3.0.CO;2-Y.
Liu JG, Xin Z. Convergence of a Galerkin method for 2-D discontinuous Euler flows. Communications on Pure and Applied Mathematics. 2000 Jan 1;53(6):786–798.
Journal cover image

Published In

Communications on Pure and Applied Mathematics

DOI

10.1002/(SICI)1097-0312(200006)53:6<786::AID-CPA3>3.0.CO;2-Y

ISSN

0010-3640

Publication Date

January 1, 2000

Volume

53

Issue

6

Start / End Page

786 / 798

Related Subject Headings

  • General Mathematics
  • 4904 Pure mathematics
  • 4901 Applied mathematics