Numerical Solving a Boundary Value Problem for the Eikonal Equation

  • Alexander G. Churbanov
  • Petr N. VabishchevichEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11386)


In the present work, a Dirichlet problem is studied for the eikonal equation. A nonlinear boundary value problem formulated here can be treated as the limit of the diffusion–reaction problem with a diffusion parameter tending to zero. For numerical solving the singularly perturbed diffusion–reaction problem, monotone approximations are used. Predictions for a 3D model problem are presented to demonstrate possibilities of the developed numerical algorithm. The standard piecewise-linear finite-element approximation is employed to constructed discretization in space.


Eikonal equation Finite-element method Diffusion–reaction equation Singularly perturbed boundary value problem Monotone approximation 



Petr Vabishchevich gratefully acknowledges support from the the Russian Federation Government (# 14.Y26.31.0013).


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Alexander G. Churbanov
    • 1
  • Petr N. Vabishchevich
    • 1
    • 2
    Email author
  1. 1.Nuclear Safety InstituteRussian Academy of SciencesMoscowRussia
  2. 2.North–Eastern Federal UniversityYakutskRussia

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