Construction and Analysis of Optimal Hierarchic Models of Boundary Value Problems on Thin Circular and Spherical Geometries
Mark Andrew Ainsworth, Mark Arnold · SIAM Journal on Scientific Computing · 2000
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.