## Abstract

In this article, we discuss a numerical method for the computation of the minimal and maximal solutions of a steady scalar Eikonal equation. This method relies on a penalty treatment of the nonlinearity, a biharmonic regularization of the resulting variational problem, and the time discretization by operator-splitting of an initial value problem associated with the Euler-Lagrange equations of the regularized variational problem. A low-order finite element discretization is advocated since it is well-suited to the low regularity of the solutions. Numerical experiments show that the method sketched above can capture efficiently the extremal solutions of various two-dimensional test problems and that it has also the ability of handling easily domains with curved boundaries.

Original language | English |
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Pages (from-to) | 659-688 |

Number of pages | 30 |

Journal | Chinese Annals of Mathematics. Series B |

Volume | 36 |

Issue number | 5 |

DOIs | |

Publication status | Published - 8 Sep 2015 |

## Scopus Subject Areas

- Mathematics(all)
- Applied Mathematics

## User-Defined Keywords

- Dynamical flow
- Eikonal equation
- Finite element methods
- Minimal and maximal solutions
- Operator splitting
- Penalization of equality constraints
- Regularization methods