Numerical Solving a Boundary Value Problem for the Eikonal Equation

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.