Publication

Numerical methods for conservation laws with rough flux

Hakon Andreas Hoel
2020
Journal Articles

Abstract

Finite volume methods are proposed for computing approximate pathwise entropy/kinetic solutions to conservation laws with flux functions driven by low-regularity paths. For a convex flux, it is demonstrated that driving path oscillations may lead to "cancellations" in the solution. Making use of this property, we show that for alpha-Holder continuous paths the convergence rate of the numerical methods can improve from O(COST-gamma), for some gamma is an element of [alpha/(12 - 8 alpha), alpha/(10 - 6 alpha)], with alpha is an element of (0, 1), to O(COST-min(1/4,alpha/2)). Numerical examples support the theoretical results.

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https://infoscience.epfl.ch/entities/publication/6d6832d1-2433-4ee7-803e-63c1f59bb81d

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Hakon Andreas Hoel
2020
Journal Articles

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/6d6832d1-2433-4ee7-803e-63c1f59bb81d

About this result

Related concepts (20)

Numerical methods for ordinary differential equations

Numerical methods for ordinary differential equations are methods used to find numerical approximations to the solutions of ordinary differential equations (ODEs). Their use is also known as "numerical integration", although this term can also refer to the computation of integrals. Many differential equations cannot be solved exactly. For practical purposes, however – such as in engineering – a numeric approximation to the solution is often sufficient. The algorithms studied here can be used to compute such an approximation.

Numerical methods for partial differential equations

Numerical methods for partial differential equations is the branch of numerical analysis that studies the numerical solution of partial differential equations (PDEs). In principle, specialized methods for hyperbolic, parabolic or elliptic partial differential equations exist. Finite difference method In this method, functions are represented by their values at certain grid points and derivatives are approximated through differences in these values.

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