
Multilevel Monte Carlo Finite Volume Methods for Random Conservation Laws with Discontinuous Flux
We consider a random scalar hyperbolic conservation law in one spatial d...
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Fluxstability for conservation laws with discontinuous flux and convergence rates of the front tracking method
We prove that adapted entropy solutions of scalar conservation laws with...
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A Godunov type scheme and error estimates for multidimensional scalar conservation laws with Panovtype discontinuous flux
This article concerns a scalar multidimensional conservation law where t...
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Convergence rates of monotone schemes for conservation laws with discontinuous flux
We prove that a class of monotone finite volume schemes for scalar conse...
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A Discrete and Continuum Model of Data Flow
We present a simplified model of data flow on processors in a high perfo...
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Convergence of a Godunov scheme for degenerate conservation laws with BV spatial flux and a study of Panov type fluxes
In this article we prove convergence of the Godunov scheme of [16] for a...
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A mathematical model of asynchronous data flow in parallel computers
We present a simplified model of data flow on processors in a high perfo...
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Scalar conservation laws with stochastic discontinuous flux function
A variety of realworld applications are modeled via hyperbolic conservation laws. To account for uncertainties or insufficient measurements, random coefficients may be incorporated. These random fields may depend discontinuously on the state space, e.g., to represent permeability in a heterogeneous or fractured medium. We introduce a suitable admissibility criterion for the resulting stochastic discontinuousflux conservation law and prove its wellposedness. Therefore, we ensure the pathwise existence and uniqueness of the corresponding deterministic setting and present a novel proof for the measurability of the solution, since classical approaches fail in the discontinuousflux case. As an example of the developed theory, we present a specific advection coefficient, which is modeled as a sum of a continuous random field and a pure jump field. This random field is employed in the stochastic conservation law, in particular a stochastic Burgers' equation, for numerical experiments. We approximate the solution to this problem via the Finite Volume method and introduce a new meshing strategy that accounts for the resulting standing wave profiles caused by the fluxdiscontinuities. The ability of this new meshing method to reduce the samplewise variance is demonstrated in numerous numerical investigations.
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