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

Djebar Baroudi

Research output: Contribution to journalArticleProfessional

Abstract

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.
Original languageEnglish
Pages (from-to)75-86
JournalRakenteiden Mekaniikka
Volume29
Issue number3-4
Publication statusPublished - 1996
MoE publication typeD1 Article in a trade journal

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Heat conduction
Temperature distribution
Polynomials
Boundary conditions
Finite element method

Cite this

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

In: Rakenteiden Mekaniikka, Vol. 29, No. 3-4, 1996, p. 75-86.

Research output: Contribution to journalArticleProfessional

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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.

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