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On the numerical solution of convection-dominated problems using hierarchical matrices
The aim of this article is to shows that hierarchical matrices ($\H$-matrices) provide a means to efficiently precondition linear systems arising from the streamline diffusion finite-element method applied to convection-dominated problems. Approximate inverses and approximate $LU$ decompositions can be computed with logarithmic-linear complexity in the standard $\H$-matrix format. Neither the complexity of the preconditioner nor the number of iterations will depend on the dominance. Although the established theory is only valid for irrotational convection, numerical experiments show that the same efficiency can be observed for general convection terms.