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Volume 3, Issue 3
Absorbing Boundary Conditions for Hyperbolic Systems

Matthias Ehrhardt

DOI: 10.4208/nmtma.2010.33.3

Numer. Math. Theor. Meth. Appl., 3 (2010), pp. 295-337.

Published online: 2010-03

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  • Abstract

This paper deals with absorbing boundary conditions for hyperbolic systems in one and two space dimensions. We prove the strict well-posedness of the resulting initial boundary value problem in 1D. Afterwards we establish the GKS-stability of the corresponding Lax-Wendroff-type finite difference scheme. Hereby, we have to extend the classical proofs, since the (discretized) absorbing boundary conditions do not fit the standard form of boundary conditions for hyperbolic systems.

  • Keywords

Absorbing boundary conditions, hyperbolic system, Engquist and Majda approach, strict well-posedness, GKS-stability.

  • AMS Subject Headings

65M06, 35L50

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{NMTMA-3-295, author = {Matthias Ehrhardt}, title = {Absorbing Boundary Conditions for Hyperbolic Systems}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2010}, volume = {3}, number = {3}, pages = {295--337}, abstract = {

This paper deals with absorbing boundary conditions for hyperbolic systems in one and two space dimensions. We prove the strict well-posedness of the resulting initial boundary value problem in 1D. Afterwards we establish the GKS-stability of the corresponding Lax-Wendroff-type finite difference scheme. Hereby, we have to extend the classical proofs, since the (discretized) absorbing boundary conditions do not fit the standard form of boundary conditions for hyperbolic systems.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.2010.33.3}, url = {http://global-sci.org/intro/article_detail/nmtma/6001.html} }
TY - JOUR T1 - Absorbing Boundary Conditions for Hyperbolic Systems AU - Matthias Ehrhardt JO - Numerical Mathematics: Theory, Methods and Applications VL - 3 SP - 295 EP - 337 PY - 2010 DA - 2010/03 SN - 3 DO - http://doi.org/10.4208/nmtma.2010.33.3 UR - https://global-sci.org/intro/article_detail/nmtma/6001.html KW - Absorbing boundary conditions, hyperbolic system, Engquist and Majda approach, strict well-posedness, GKS-stability. AB -

This paper deals with absorbing boundary conditions for hyperbolic systems in one and two space dimensions. We prove the strict well-posedness of the resulting initial boundary value problem in 1D. Afterwards we establish the GKS-stability of the corresponding Lax-Wendroff-type finite difference scheme. Hereby, we have to extend the classical proofs, since the (discretized) absorbing boundary conditions do not fit the standard form of boundary conditions for hyperbolic systems.

Matthias Ehrhardt. (2010). Absorbing Boundary Conditions for Hyperbolic Systems. Numerical Mathematics: Theory, Methods and Applications. 3 (3). 295-337. doi:10.4208/nmtma.2010.33.3
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