## 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

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

## Published In

Communications on Pure and Applied Mathematics

## DOI

## 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
- 0102 Applied Mathematics
- 0101 Pure Mathematics

### Citation

APA

Chicago

ICMJE

MLA

NLM

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-YLiu, 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.

## Published In

Communications on Pure and Applied Mathematics

## DOI

## 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
- 0102 Applied Mathematics
- 0101 Pure Mathematics