### Abstract

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

Pages (from-to) | 75-86 |

Journal | Rakenteiden Mekaniikka |

Volume | 29 |

Issue number | 3-4 |

Publication status | Published - 1996 |

MoE publication type | D1 Article in a trade journal |

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### Cite this

*Rakenteiden Mekaniikka*,

*29*(3-4), 75-86.

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*Rakenteiden Mekaniikka*, vol. 29, no. 3-4, pp. 75-86.

**Application of hp-finite element formulation to non-linear heat conduction problems with source terms.** / Baroudi, Djebar.

Research output: Contribution to journal › Article › Professional

TY - JOUR

T1 - Application of hp-finite element formulation to non-linear heat conduction problems with source terms

AU - Baroudi, Djebar

PY - 1996

Y1 - 1996

N2 - This work presents an application of the hp- finite element formulation to solve the general non-linear heat conduction problem in a solid for cases involving heat sources and non-linear boundary conditions terms. The temperature field is semi-discretized in space with hierarchical basis functions formed using the orthogonal Legendre polynomials. The good approximation properties of the hp-finite element method are achieved here by the combined effect of the traditional mesh refinement together with the p-extension of the polynomial basis. Because the temperature field is continuous, the hp-formulation performs very well. The calculated temperature field converges much faster in the hp-version than the traditional h-refinement. In general, the h-refinement is used for regions with non-smooth solution and the p-extension for the smooth ones. This work also shows a systematic way to treat source terms and the possible non-linear natural boundary conditions present in the heat conduction equation by including them in the force vector of the discretized heat conduction equation.

AB - This work presents an application of the hp- finite element formulation to solve the general non-linear heat conduction problem in a solid for cases involving heat sources and non-linear boundary conditions terms. The temperature field is semi-discretized in space with hierarchical basis functions formed using the orthogonal Legendre polynomials. The good approximation properties of the hp-finite element method are achieved here by the combined effect of the traditional mesh refinement together with the p-extension of the polynomial basis. Because the temperature field is continuous, the hp-formulation performs very well. The calculated temperature field converges much faster in the hp-version than the traditional h-refinement. In general, the h-refinement is used for regions with non-smooth solution and the p-extension for the smooth ones. This work also shows a systematic way to treat source terms and the possible non-linear natural boundary conditions present in the heat conduction equation by including them in the force vector of the discretized heat conduction equation.

M3 - Article

VL - 29

SP - 75

EP - 86

JO - Rakenteiden Mekaniikka

JF - Rakenteiden Mekaniikka

SN - 0783-6104

IS - 3-4

ER -