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Volume 17, Issue 3
An Adaptive Viscosity E–Scheme for Degenerate Conservation and Balance Laws

Ebise Adugna Abdi & Hans Joachim Schroll

Int. J. Numer. Anal. Mod., 17 (2020), pp. 434-456.

Published online: 2020-05

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  • Abstract

An adaptive E–scheme for degenerate, viscous balance laws is presented. Taking into account natural diffusion, numerical viscosity is locally reduced to a minimum. Numerical experiments demonstrate the improved accuracy of the adaptive scheme. Explicit and implicit three–point E–schemes are monotone, TVD and nonlinearly stable. A high–resolution version of the adaptive E–scheme is derived and tested in experiments. The latter is not necessarily monotone, but TVD.

  • Keywords

Balance law, E–scheme, monotone, degenerate viscosity.

  • AMS Subject Headings

35K65, 35L65, 65M06, 65M08

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

ebiatye2020@gmail.com (Ebise Adugna Abdi)

achim@imada.sdu.dk (Hans Joachim Schroll)

  • BibTex
  • RIS
  • TXT
@Article{IJNAM-17-434, author = {Adugna Abdi , Ebise and Joachim Schroll , Hans}, title = {An Adaptive Viscosity E–Scheme for Degenerate Conservation and Balance Laws}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2020}, volume = {17}, number = {3}, pages = {434--456}, abstract = {

An adaptive E–scheme for degenerate, viscous balance laws is presented. Taking into account natural diffusion, numerical viscosity is locally reduced to a minimum. Numerical experiments demonstrate the improved accuracy of the adaptive scheme. Explicit and implicit three–point E–schemes are monotone, TVD and nonlinearly stable. A high–resolution version of the adaptive E–scheme is derived and tested in experiments. The latter is not necessarily monotone, but TVD.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/16867.html} }
TY - JOUR T1 - An Adaptive Viscosity E–Scheme for Degenerate Conservation and Balance Laws AU - Adugna Abdi , Ebise AU - Joachim Schroll , Hans JO - International Journal of Numerical Analysis and Modeling VL - 3 SP - 434 EP - 456 PY - 2020 DA - 2020/05 SN - 17 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/16867.html KW - Balance law, E–scheme, monotone, degenerate viscosity. AB -

An adaptive E–scheme for degenerate, viscous balance laws is presented. Taking into account natural diffusion, numerical viscosity is locally reduced to a minimum. Numerical experiments demonstrate the improved accuracy of the adaptive scheme. Explicit and implicit three–point E–schemes are monotone, TVD and nonlinearly stable. A high–resolution version of the adaptive E–scheme is derived and tested in experiments. The latter is not necessarily monotone, but TVD.

Adugna Abdi , Ebise and Joachim Schroll , Hans. (2020). An Adaptive Viscosity E–Scheme for Degenerate Conservation and Balance Laws. International Journal of Numerical Analysis and Modeling. 17 (3). 434-456. doi:
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