Accuracy of the domain material derivative approach to shape design sensitivities

Numerical accuracy for the boundary and domain methods of the material derivative approach to shape design sensitivities is investigated through the use of mesh refinement. The results show that the domain method is generally more accurate than the boundary method using the finite-element technique. It is also shown that the domain method is equivalent, under certain assumptions, to the direct differentiation approach that evaluates sensitivities by directdifferentiating the implicit discretized equilibrium equation, not only theoretically but also numerically.