Volume 53, Number 5, September-October 2019
|Page(s)||1459 - 1476|
|Published online||23 July 2019|
Convergence of the finite volume method on a Schwarzschild background
Laboratoire Jacques-Louis Lions, Centre National de la Recherche Scientifique Sorbonne Université, 4, Place Jussieu, 75252 Paris, France
* Corresponding author: email@example.com
Accepted: 7 May 2019
We introduce a class of nonlinear hyperbolic conservation laws on a Schwarzschild black hole background and derive several properties satisfied by (possibly weak) solutions. Next, we formulate a numerical approximation scheme which is based on the finite volume methodology and takes the curved geometry into account. An interesting feature of our model is that no boundary conditions is required at the black hole horizon boundary. We establish that this scheme converges to an entropy weak solution to the initial value problem and, in turn, our analysis also provides us with a theory of existence and stability for a new class of conservation laws.
Mathematics Subject Classification: 35L60 / 65M05 / 76L05
Key words: Hyperbolic conservation law / Schwarzschild black hole / weak solution / finite volume scheme / convergence analysis
© The authors. Published by EDP Sciences, SMAI 2019
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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