Journal of Maternal-Fetal and Neonatal Medicine.
Taylor and Francis Ltd.
2019.
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.
Authors
Churbanov A.G.1
,
Vabishchevich P.N.
1,
2
Publisher
Elsevier B.V.
Language
English
Pages
55-67
Status
Published
Link
Volume
362
Year
2019
Organizations
- 1 Nuclear Safety Institute, Russian Academy of Sciences, 52, B. Tulskaya, Moscow, Russian Federation
- 2 Peoples’ Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya St, Moscow, Russian Federation
Keywords
Diffusion–reaction equation; Eikonal equation; Finite-element method; Monotone approximation; Singularly perturbed BVP
Share
Other records
Nonlinear Analysis: Real World Applications.
Elsevier Ltd.
Vol. 50.
2019.
P. 603-612