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Convergent semi-explicit scheme to a non-linear eikonal system
  • Maryam Al Zohbi ,
  • Ahmad EL HAJJ,
  • Mustapha Jazar
Maryam Al Zohbi
Université de Technologie de Compiègne
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Ahmad EL HAJJ
Université de Technologie de Compiègne

Corresponding Author:[email protected]

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Mustapha Jazar
LaMA-Liban, Lebanese University
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Abstract

We consider a system of non-linear eikonal equations in one space dimension that describes the evolution of interfaces moving with non-signed strongly coupled velocities. We have recently proven the global existence and uniqueness of viscosity solutions for this system, under a BV estimate. In this paper, we propose a semi-explicit scheme that satisfies the same BV estimate proven in the continuous case, at the discrete level, and we show that a certain linear interpolation of the discrete solution to the scheme converges to a viscosity solution of the main system considered. We also provide some numerical simulations in the case of dislocations dynamics