### Abstract

Language | English |
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Place of Publication | Glasgow |

Publisher | University of Strathclyde |

Number of pages | 17 |

Volume | 2011-16 |

Publication status | Published - 2011 |

### Fingerprint

### Keywords

- robust
- adaptive computation
- one-dimensional
- q-tensor model
- nematic liquid crystals
- uniform convergence
- adaptive grids
- mesh equidistribution
- monitor function

### Cite this

*Robust adaptive computation of a one-dimensional Q-tensor model of nematic liquid crystals*. Glasgow: University of Strathclyde.

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

Research output: Working paper

TY - UNPB

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

PY - 2011

Y1 - 2011

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 soluction converges at an otimal 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 soluction converges at an otimal rate with respect to the mesh density and that the solution accuracy is robust to the size of singular perturbation parameter

KW - robust

KW - adaptive computation

KW - one-dimensional

KW - q-tensor model

KW - nematic liquid crystals

KW - uniform convergence

KW - adaptive grids

KW - mesh equidistribution

KW - monitor function

UR - http://www.mathstat.strath.ac.uk/research/reports/2011

M3 - Working paper

VL - 2011-16

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

PB - University of Strathclyde

CY - Glasgow

ER -