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

摘要

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. (C) 2019 Elsevier B.V. All rights reserved.