Abstract
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.
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Petr Vabishchevich gratefully acknowledges support from the the Russian Federation Government (# 14.Y26.31.0013).
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Churbanov, A.G., Vabishchevich, P.N. (2019). Numerical Solving a Boundary Value Problem for the Eikonal Equation. In: Dimov, I., Faragó, I., Vulkov, L. (eds) Finite Difference Methods. Theory and Applications. FDM 2018. Lecture Notes in Computer Science(), vol 11386. Springer, Cham. https://doi.org/10.1007/978-3-030-11539-5_3
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