### Abstract

We present a method for solving nonlinear reaction-diffusion equations, s∂p/∂t-▽·(K▽p) = f(x,p), using a mixed finite-element method. To linearize the mixed-method equations, we use a two-grid scheme that relegates all of the Newton-like iterations to grids much coarser than the original one, with no loss in order of accuracy. The use of a multigrid-based solver for the indefinite linear systems that arise at each iteration, as well as for the similar system that arises on the fine grid, allows for even greater efficiency.

Original language | English |
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Pages | 617-623 |

Number of pages | 7 |

Publication status | Published - 1998 Jan 1 |

Event | Proceedings of the 1998 12th International Conference on Computational Methods in Water Resources, CMWR XII'98. Part 1 (of 2) - Crete, Greece Duration: 1998 Jun 1 → 1998 Jun 1 |

### Other

Other | Proceedings of the 1998 12th International Conference on Computational Methods in Water Resources, CMWR XII'98. Part 1 (of 2) |
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City | Crete, Greece |

Period | 98/6/1 → 98/6/1 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Engineering(all)

### Cite this

*Mixed finite-element solution of reaction-diffusion equations using a two-grid method*. 617-623. Paper presented at Proceedings of the 1998 12th International Conference on Computational Methods in Water Resources, CMWR XII'98. Part 1 (of 2), Crete, Greece, .

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**Mixed finite-element solution of reaction-diffusion equations using a two-grid method.** / Wu, Li; Allen, Myron B.; Park, Eun Jae.

Research output: Contribution to conference › Paper

TY - CONF

T1 - Mixed finite-element solution of reaction-diffusion equations using a two-grid method

AU - Wu, Li

AU - Allen, Myron B.

AU - Park, Eun Jae

PY - 1998/1/1

Y1 - 1998/1/1

N2 - We present a method for solving nonlinear reaction-diffusion equations, s∂p/∂t-▽·(K▽p) = f(x,p), using a mixed finite-element method. To linearize the mixed-method equations, we use a two-grid scheme that relegates all of the Newton-like iterations to grids much coarser than the original one, with no loss in order of accuracy. The use of a multigrid-based solver for the indefinite linear systems that arise at each iteration, as well as for the similar system that arises on the fine grid, allows for even greater efficiency.

AB - We present a method for solving nonlinear reaction-diffusion equations, s∂p/∂t-▽·(K▽p) = f(x,p), using a mixed finite-element method. To linearize the mixed-method equations, we use a two-grid scheme that relegates all of the Newton-like iterations to grids much coarser than the original one, with no loss in order of accuracy. The use of a multigrid-based solver for the indefinite linear systems that arise at each iteration, as well as for the similar system that arises on the fine grid, allows for even greater efficiency.

UR - http://www.scopus.com/inward/record.url?scp=0031699850&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0031699850&partnerID=8YFLogxK

M3 - Paper

AN - SCOPUS:0031699850

SP - 617

EP - 623

ER -