By J M T Thompson; G W Hunt
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It is precisely this that leads to the more quantitative basis used here. Your question gives me a chance to say something I should have mentioned during the lecture. The problem with error estimation generally is the rather large cost of adding good error estimates into the program. With hierarchical projection, we have to do quite a bit of extra programming to obtain the local changes, and then integrals have to be carried out on an element-by-element basis, involving a special projection of residual integrals.
While more refined finite element grids and higher order elements would improve results obtained using the boundary method, superiority of the domain method in this application is clear. The drastically superior performance of the domain approach in the interface problem is repeated in a number of applications of design sensitivity theory to built-up structures that are composed of multiple components. Numerical experimentation with a beam-plate-truss built-up structure  and with a threedimensional box structure  has illustrated the superiority of the domain method over the boundary approach.
CRAIG, J. Z. ZHU and R. H. GALLAGHER of slender proportions, I believe we are very close to the exact solution using the beam theory. It was on that basis that the local efficiency (the micro efficiency ) was calculated. On the L-shaped domain, it was an exact solution which was used to find the total energy norm error which included singularities. Vasilopoulos My second question regards the theoretical basis for taking the difference between the smoothed and the direct value as an estimate of the local stresses.
A general theory of elastic stability by J M T Thompson; G W Hunt