Numerical solution of boundary value problems for the eikonal equation in an anisotropic medium

A Dirichlet problem is considered for the eikonal equation in an anisotropic medium. The nonlinear boundary value problem (BVP)formulated in the present work is the limit of the diffusion–reaction problem with a diffusion parameter tending to zero. To solve numerically the singularly perturbed diffusion–reaction problem, monotone approximations are employed. Numerical examples are presented for a two-dimensional BVP for the eikonal equation in an anisotropic medium. The standard Lagrangian finite-element approximation in space is used in computations. © 2019 Elsevier B.V.