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A comparison of boundary element method formulations for steady state anisotropic heat conduction problems. (English) Zbl 0982.80009
Summary: The boundary element method (BEM) is numerically implemented in order to solve steady state anisotropic heat conduction problems. Various types of elements, namely, constant elements, continuous and discontinuous linear elements and continuous and discontinuous quadratic elements are used. The performances of these various BEM formulations are compared for both the direct well-posed Dirichlet problem and the inverse ill-posed Cauchy problem, revealing several features of the BEM. Furthermore, previously undetermined analytical solutions for the integrals associated with linear and quadratic elements are presented.

80M15 Boundary element methods applied to problems in thermodynamics and heat transfer
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