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.

[发布日期] 2019-12-15

[关键词] Eikonal equation;Finite-element method;Diffusion-reaction equation;Singularly perturbed BVP;Monotone approximation