## Abstract

Orthogonal maps are the solutions of the mathematical model of paper-folding, also called the origami problem. They consist of a system of first-order fully nonlinear equations involving the gradient of the solution. The Dirichlet problem for orthogonal maps is considered here. A variational approach is advocated for the numerical approximation of the maps. The introduction of a suitable objective function allows us to enforce the uniqueness of the solution. A strategy based on a splitting algorithm for the corresponding flow problem is presented and leads to decoupling the time-dependent problem into a sequence of local nonlinear problems and a global linear variational problem at each time step. Numerical experiments validate the accuracy and the efficiency of the method for various domains and meshes.

Original language | English |
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Pages (from-to) | B1341-B1367 |

Number of pages | 27 |

Journal | SIAM Journal on Scientific Computing |

Volume | 41 |

Issue number | 6 |

DOIs | |

Publication status | Published - 10 Dec 2019 |

## Scopus Subject Areas

- Computational Mathematics
- Applied Mathematics

## User-Defined Keywords

- Dynamical flow
- Eikonal equation
- Finite element methods
- Operator splitting
- Origami
- Orthogonal maps