A posteriori error estimates for the effective Hamiltonian of dislocation dynamics

Cacace, Simone; Chambolle, Antonin; Monneau, Régis

doi:10.1007/s00211-011-0430-z

Cited by 9 publications

(20 citation statements)

References 24 publications

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“…This approximation allows us to compute the approximation of the flux limiter. This algorithm inspired by the one by Cacace et al [6] (used for dislocations dynamics) and justified by the results in Appendix A can be adapted for other pdes given that the numerical scheme satisfies similar conditions to the ones we have in our scenario.…”

Section: Resultsmentioning

confidence: 72%

“…However, the form of this pde allowed us to use very interesting numerical analysis techniques. We used a numerical scheme inspired by the ones of Cacace et al [6], Costeseque et al [7] and Forcadel [11] (used for traffic flow and dislocations dynamics). The techniques we use can be used to discretise non-local operators and non-linear terms.…”

Section: Resultsmentioning

confidence: 99%

“…The numerical scheme we use was inspired by one from Cacace et al [6], and from Forcadel [11] for the non-local operator, and by Costeseque et al [7] E61 for the local operator. We consider a uniform grid of the interval [−l, l] with 2n + 1 points, n ∈ N\{0}, and we denote by ∆x = l/n the discretization step.…”

Section: Discretization Of (9)mentioning

confidence: 99%

“…Similarly to Cacace et al [6], we consider the following Osher-Sethian [21] upwind discretization of the modulus of the gradient. Let S = (p, q) ∈ R 2 , we define the following function, that we use for the discretization of the gradient…”

Section: E62mentioning

confidence: 99%

“…The following algorithm is inspired by the one from Cacace et al [6], and by the results from Appendix A. The idea of the algorithm is to build the extremal solutions from Corollary 30, to build the biggest sub-solution and the smallest super-solution.…”

Section: The Algorithmmentioning

confidence: 99%

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Numerical specified homogenization of a discrete model with a local perturbation and application to traffic flow

Salazar

2018

ANZIAMJ

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We present techniques for the analysis and numerical analysis of non-local non-linear pdes. We apply these techniques to an equation derived from the modelling of traffic flow. We introduce a macroscopic model in the form of a Hamilton-Jacobi equation with a junction condition. More precisely, the goal of this work is to obtain the numerical homogenization of a non-local pde deriving from a first order discrete model for traffic flow that simulates the presence of a local perturbation. Previously we showed that the solution of the discrete microscopic model converges to the (unique) solution of a HamiltonJacobi equation posed on a network and with a junction condition (it can be seen as a flux limiter that keeps the memory of the local perturbation). The goal of this article is to provide a numerical scheme

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Section: Resultsmentioning

confidence: 72%