### Abstract

Language | English |
---|---|

Pages | 3627-3640 |

Number of pages | 14 |

Journal | Computers and Mathematics with Applications |

Volume | 64 |

Issue number | 11 |

DOIs | |

Publication status | Published - Dec 2012 |

### Fingerprint

### Keywords

- liquid crystals
- adaptive computation
- q-tensor model

### Cite this

*Computers and Mathematics with Applications*,

*64*(11), 3627-3640. https://doi.org/10.1016/j.camwa.2012.10.003

}

*Computers and Mathematics with Applications*, vol. 64, no. 11, pp. 3627-3640. https://doi.org/10.1016/j.camwa.2012.10.003

**Robust adaptive computation of a one-dimensional Q-tensor model of nematic liquid crystals.** / MacDonald, Craig; MacKenzie, John; Ramage, Alison; Newton, Chris.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Robust adaptive computation of a one-dimensional Q-tensor model of nematic liquid crystals

AU - MacDonald, Craig

AU - MacKenzie, John

AU - Ramage, Alison

AU - Newton, Chris

N1 - Additional information has been added to this entry

PY - 2012/12

Y1 - 2012/12

N2 - This paper illustrates the use of an adaptive finite element method to solve a non-linear singularly perturbed boundary value problem which arises from a one-dimensional q-tensor model of liquid crystals. The adaptive non-uniform mesh is generated by equidistribution of a strictly positive monitor function which is a linear combination of a constant floor and a power of the first derivative of the numerical solution. by an appropriate selection of the monitor function parameters, we show that the computed numerical solution converges at an optimal rate with respect to the mesh density and that the solution accuracy is robust to the size of singular perturbation parameter.

AB - This paper illustrates the use of an adaptive finite element method to solve a non-linear singularly perturbed boundary value problem which arises from a one-dimensional q-tensor model of liquid crystals. The adaptive non-uniform mesh is generated by equidistribution of a strictly positive monitor function which is a linear combination of a constant floor and a power of the first derivative of the numerical solution. by an appropriate selection of the monitor function parameters, we show that the computed numerical solution converges at an optimal rate with respect to the mesh density and that the solution accuracy is robust to the size of singular perturbation parameter.

KW - liquid crystals

KW - adaptive computation

KW - q-tensor model

UR - http://www.mathstat.strath.ac.uk/downloads/publications/16robsutadaptive-2011.pdf

U2 - 10.1016/j.camwa.2012.10.003

DO - 10.1016/j.camwa.2012.10.003

M3 - Article

VL - 64

SP - 3627

EP - 3640

JO - Computers and Mathematics with Applications

T2 - Computers and Mathematics with Applications

JF - Computers and Mathematics with Applications

SN - 0898-1221

IS - 11

ER -