An alpha-adaptive approach for stabilized finite element solution of advective-diffusive problems with sharp gradients

Abstract

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

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