An optimal error estimate for upwind Finite Volume methods for nonlinear hyperbolic conservation laws

2011 ◽  
Vol 61 (11) ◽  
pp. 1114-1131 ◽  
Author(s):  
Daniel Bouche ◽  
Jean-Michel Ghidaglia ◽  
Frédéric P. Pascal
Keyword(s):  
Error Estimate ◽  
Conservation Laws ◽  
Finite Volume ◽  
Hyperbolic Conservation Laws ◽  
Finite Volume Methods ◽  
Optimal Error Estimate ◽  
Optimal Error ◽  
Hyperbolic Conservation ◽  
Nonlinear Hyperbolic Conservation Laws

scholarly journals Convergence of the finite volume method on a Schwarzschild background

2019 ◽  
Vol 53 (5) ◽  
pp. 1459-1476
Author(s):  
Shijie Dong ◽  
Philippe G. LeFloch
Keyword(s):  
Black Hole ◽  
Conservation Laws ◽  
Finite Volume ◽  
Hyperbolic Conservation Laws ◽  
Hyperbolic Conservation ◽  
New Class ◽  
Black Hole Background ◽  
Existence And Stability ◽  
Volume Method ◽  
Nonlinear Hyperbolic Conservation Laws

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.

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