### Abstract

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

Pages | 68-78 |

Number of pages | 10 |

Publication status | Published - 2002 |

Event | Applied Mathematics Seminar - Coventry, UK Duration: 13 Jun 2003 → … |

### Conference

Conference | Applied Mathematics Seminar |
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City | Coventry, UK |

Period | 13/06/03 → … |

### Fingerprint

### Keywords

- pde
- partial differential equation
- mathematics

### Cite this

*A review of moving mesh methods for the numerical solution of PDEs*. 68-78. Paper presented at Applied Mathematics Seminar, Coventry, UK, .

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**A review of moving mesh methods for the numerical solution of PDEs.** / Sloan, D.M.

Research output: Contribution to conference › Paper

TY - CONF

T1 - A review of moving mesh methods for the numerical solution of PDEs

AU - Sloan, D.M.

N1 - University of Strathclyde Mathematics Research Report

PY - 2002

Y1 - 2002

N2 - Accurate modelling of scientific problems that are governed by partial differential equations (PDEs) with steep solution regions often involves high computational cost if a uniform mesh is used. In recent years a family of methods---moving mesh methods---has been developed that adapts the mesh to features of the computed solution. The nodal density is high in regions of high solution variation and low in regions where the solution variation is small. The talk describes moving mesh methods that are based on the idea of equidistribution (see, for example, W Huang and R D Russell, SIAM J Sci Comput 20 (1999) 998-1015). These methods utilise a PDE to evolve the mesh in a manner that accurately captures sharp fronts with a relatively small number of mesh points. The complete solution process involves the combined numerical solution of a moving mesh PDE and the governing system of physical PDEs. Numerical results are referenced to demonstrate the effectiveness of the methods.

AB - Accurate modelling of scientific problems that are governed by partial differential equations (PDEs) with steep solution regions often involves high computational cost if a uniform mesh is used. In recent years a family of methods---moving mesh methods---has been developed that adapts the mesh to features of the computed solution. The nodal density is high in regions of high solution variation and low in regions where the solution variation is small. The talk describes moving mesh methods that are based on the idea of equidistribution (see, for example, W Huang and R D Russell, SIAM J Sci Comput 20 (1999) 998-1015). These methods utilise a PDE to evolve the mesh in a manner that accurately captures sharp fronts with a relatively small number of mesh points. The complete solution process involves the combined numerical solution of a moving mesh PDE and the governing system of physical PDEs. Numerical results are referenced to demonstrate the effectiveness of the methods.

KW - pde

KW - partial differential equation

KW - mathematics

M3 - Paper

SP - 68

EP - 78

ER -