In this paper the FIC method is used as the basis for a new “alpha-adaptive”
procedure (where alpha denotes the stabilization parameters) for obtaining stable
solution in advective-diffusive problems where arbitrary sharp transverse gradients are
present. The new stabilization thechnique can be viewed as an alternative class of
adaptive methods where the numerical solution is enhanced by searching “adaptively”
the optimal value of the streamline and transverse (crosswing) stabilization parameters
while keeping the mesh and the finite element approximation unchanged. Indeed the
basic alpha-adaptive process can be enhanced by combining it with standard h, p or hp
adaptive schemes.
In the first part of the paper the basis of the FIC stabilized method for advectivediffusive problems are explained. Next the algorithm for computing the streamline and
transverse stabilization parameters via the new “alpha-adaptive” procedure is described.
Finally, the efficiency and accuracy of the new approach are shown in two examples of
application.

Published in New Advances in Adaptive Computational Methods in Mechanics, P. Ladeveze and J.T. Oden (Eds.), Elsevier, 1998
DOI: 10.1016/S0922-5382(98)80017-2