## Abstract

This paper is an extension of the preceding study (Nakao, this journal, 1991) in which we described a numerical verification method of the solution for one-space dimensional parabolic problems, to the several-space dimensional case. Here, numerical verification means the automatic proof of the existence of solutions to the problems by some numerical techniques on a computer. We reformulate the verification condition for nonlinear parabolic initial boundary value problems using the fixed-point problem of a compact operator on certain function spaces. As in the preceding study based upon a simple C^{0} finite-element approximation and its constructive a priori error estimates, a numerical verification procedure is presented with some numerical examples.

Original language | English |
---|---|

Pages (from-to) | 401-410 |

Number of pages | 10 |

Journal | Journal of Computational and Applied Mathematics |

Volume | 50 |

Issue number | 1-3 |

DOIs | |

Publication status | Published - 1994 May 20 |

Externally published | Yes |

## Keywords

- Error estimates
- Finite-element method
- Fixed-point theorem
- Parabolic problem

## ASJC Scopus subject areas

- Applied Mathematics
- Computational Mathematics
- Numerical Analysis