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Volume 11, Issue 1
Convergence of a Relaxation Scheme for a 2×2 Triangular System of Conservation Laws

C. Agrell & N. H. Risebro

Int. J. Numer. Anal. Mod., 11 (2014), pp. 148-171.

Published online: 2014-11

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  • Abstract

We study relaxation approximations to solutions of a 2 × 2 triangular system of conservation laws. We show that smooth relaxation approximations exist for all time. A finite difference approximation of the relaxation system gives rise to a relaxation scheme of the Jin and Xin type. In both cases we show that a sequence of approximate solutions is produced where the limit is a weak solution of the triangular system. Compensated compactness is used to establish convergence.

  • Keywords

triangular systems of conservation laws, relaxation, compensated compactness.

  • AMS Subject Headings

35L45, 35L40, 65M06

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-11-148, author = {Agrell , C. and Risebro , N. H.}, title = {Convergence of a Relaxation Scheme for a 2×2 Triangular System of Conservation Laws}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2014}, volume = {11}, number = {1}, pages = {148--171}, abstract = {

We study relaxation approximations to solutions of a 2 × 2 triangular system of conservation laws. We show that smooth relaxation approximations exist for all time. A finite difference approximation of the relaxation system gives rise to a relaxation scheme of the Jin and Xin type. In both cases we show that a sequence of approximate solutions is produced where the limit is a weak solution of the triangular system. Compensated compactness is used to establish convergence.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/519.html} }
TY - JOUR T1 - Convergence of a Relaxation Scheme for a 2×2 Triangular System of Conservation Laws AU - Agrell , C. AU - Risebro , N. H. JO - International Journal of Numerical Analysis and Modeling VL - 1 SP - 148 EP - 171 PY - 2014 DA - 2014/11 SN - 11 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/519.html KW - triangular systems of conservation laws, relaxation, compensated compactness. AB -

We study relaxation approximations to solutions of a 2 × 2 triangular system of conservation laws. We show that smooth relaxation approximations exist for all time. A finite difference approximation of the relaxation system gives rise to a relaxation scheme of the Jin and Xin type. In both cases we show that a sequence of approximate solutions is produced where the limit is a weak solution of the triangular system. Compensated compactness is used to establish convergence.

C. Agrell & N. H. Risebro. (2019). Convergence of a Relaxation Scheme for a 2×2 Triangular System of Conservation Laws. International Journal of Numerical Analysis and Modeling. 11 (1). 148-171. doi:
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