### Abstract

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

Number of pages | 27 |

Journal | SIAM Journal on Scientific Computing |

State | Accepted/In press - 3 Jan 2019 |

### Fingerprint

### Keywords

- geometric partial differential equations
- monitor functions
- tangential redistribution
- moving mesh methods
- forced curve shortening flow

### Cite this

*SIAM Journal on Scientific Computing*.

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**An adaptive moving mesh method for forced curve shortening flow.** / Mackenzie, J.A.; Nolan, M.; Rowlatt, C.F.; Insall, R.H.

Research output: Contribution to journal › Article

TY - JOUR

T1 - An adaptive moving mesh method for forced curve shortening flow

AU - Mackenzie,J.A.

AU - Nolan,M.

AU - Rowlatt,C.F.

AU - Insall,R.H.

PY - 2019/1/3

Y1 - 2019/1/3

N2 - We propose a novel adaptive moving mesh method for the numerical solution of a forced curve shortening geometric evolution equation. Control of the mesh quality is obtained using a tangential mesh velocity derived from a mesh equidistribution principle, where a positive adaptivity measure or monitor function is approximately equidistributed along the evolving curve. Central finite differences are used to discretise in space the governing evolution equation for the position vector and a second-order implicit scheme is used for the temporal integration. Simulations are presented indicating the generation of meshes which resolve areas of high curvature and are of second-order accuracy. Furthermore, the new method delivers improved solution accuracy compared to the use of uniform arc-length meshes.

AB - We propose a novel adaptive moving mesh method for the numerical solution of a forced curve shortening geometric evolution equation. Control of the mesh quality is obtained using a tangential mesh velocity derived from a mesh equidistribution principle, where a positive adaptivity measure or monitor function is approximately equidistributed along the evolving curve. Central finite differences are used to discretise in space the governing evolution equation for the position vector and a second-order implicit scheme is used for the temporal integration. Simulations are presented indicating the generation of meshes which resolve areas of high curvature and are of second-order accuracy. Furthermore, the new method delivers improved solution accuracy compared to the use of uniform arc-length meshes.

KW - geometric partial differential equations

KW - monitor functions

KW - tangential redistribution

KW - moving mesh methods

KW - forced curve shortening flow

UR - https://epubs.siam.org/journal/sjoce3

M3 - Article

JO - SIAM Journal on Scientific Computing

T2 - SIAM Journal on Scientific Computing

JF - SIAM Journal on Scientific Computing

SN - 1064-8275

ER -