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Arbitrary Lagrangian-Eulerian discontinuous Galerkin method for conservation laws on moving simplex meshes


Authors: Pei Fu, Gero Schnücke and Yinhua Xia
Journal: Math. Comp. 88 (2019), 2221-2255
MSC (2010): Primary 35L65, 65M60
DOI: https://doi.org/10.1090/mcom/3417
Published electronically: March 5, 2019
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Additional Information

Pei Fu
Affiliation: School of Mathematical Sciences, University of Science and Technology of China, Hefei, Anhui 230026, People’s Republic of China
Email: sxfp2013@mail.ustc.edu.cn

Gero Schnücke
Affiliation: Mathematical Institute, University of Cologne, Weyertal 86-90, 50931 Köln, Germany
Email: gschnuec@math.uni-koeln.de

Yinhua Xia
Affiliation: School of Mathematical Sciences, University of Science and Technology of China, Hefei, Anhui 230026, People’s Republic of China
Email: yhxia@ustc.edu.cn

DOI: https://doi.org/10.1090/mcom/3417
Keywords: Arbitrary Lagrangian-Eulerian discontinuous Galerkin method, conservation laws, moving simplex meshes, geometric conservation law, $\mathrm{L}^2$-stability, error estimates, maximum principle
Received by editor(s): April 10, 2018
Received by editor(s) in revised form: September 29, 2018
Published electronically: March 5, 2019
Additional Notes: The third author’s research was supported by NSFC grants No. 11871449 and No. 11471306, and a grant from the Science & Technology on Reliability & Environmental Engineering Laboratory (No. 6142A0502020817).
The third author is the corresponding author.
Article copyright: © Copyright 2019 American Mathematical Society