MESHLESS LOCAL PETROV-GALERKIN METHOD FOR NONLINEAR HEAT CONDUCTION PROBLEMS

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Author list: Thakur H, Singh KM, Sahoo PK

Publisher: Taylor & Francis: STM, Behavioural Science and Public Health Titles

Place: PHILADELPHIA

Publication year: 2009

Journal: Numerical Heat Transfer, Part B Fundamentals (1040-7790)

Journal acronym: NUMER HEAT TR B-FUND

Volume number: 56

Issue number: 5

Start page: 393

End page: 410

Number of pages: 18

ISSN: 1040-7790

eISSN: 1521-0626

Languages: English-Great Britain (EN-GB)

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Abstract

The meshless local Petrov-Galerkin (MLPG) method is an effective meshless method to solve partial differential equations. In this article, the MLPG method is used to solve nonlinear steady and transient heat conduction problems. The essential boundary condition is enforced by the method of direct interpolation. The moving least-squares (MLS) method is used for interpolation. Thermal conductivity of the material is assumed to be dependent on the temperature. An iterative procedure based on the predictor-corrector method is used. Time integration is performed using the h method. Results are compared with the available exact solution and the solution by the finite-element method, and is found to be in good agreement.

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