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Construction and analysis of optimal hierarchic models of boundary value problems on thin circular and spherical geometries. (English) Zbl 1049.65135

Summary: A sequence of optimal hierarchic models is derived for stationary heat conduction on the following laminated domains: a flat plate, a circular arch, and a spherical shell. An a priori bound is presented, which is evaluated explicitly in the homogeneous case on each domain. Computational examples are given, which illustrate the theoretical results. Furthermore, in the case of a spherical shell, the hierarchic models are compared numerically to models obtained using polynomial approximation in the radial direction, and it is found that the hierarchic models are both more accurate than the polynomial ones and provide more robust convergence with respect to the shell thickness.

MSC:

65N35 Spectral, collocation and related methods for boundary value problems involving PDEs
80A20 Heat and mass transfer, heat flow (MSC2010)
80M25 Other numerical methods (thermodynamics) (MSC2010)
74S30 Other numerical methods in solid mechanics (MSC2010)
74K25 Shells
74K20 Plates
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
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