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Convergent semi-explicit scheme to a non-linear eikonal system

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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 dislocation dynamics.

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Authors and Affiliations

  1. Université de Technologie de Compiègne, LMAC, 60205, Compiègne Cedex, France

    Maryam Al Zohbi & Ahmad El Hajj

  2. Université Libanaise, LaMA, Tripoli, Lebanon

    Maryam Al Zohbi & Mustapha Jazar

Authors
  1. Maryam Al Zohbi
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  2. Ahmad El Hajj
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  3. Mustapha Jazar
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Correspondence to Ahmad El Hajj.

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Communicated by Ragnar Winther.

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Zohbi, M.A., Hajj, A.E. & Jazar, M. Convergent semi-explicit scheme to a non-linear eikonal system. Bit Numer Math 62, 1841–1872 (2022). https://doi.org/10.1007/s10543-022-00933-z

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