H-matrices for convection-diffusion problems with constant convection

Authors:
Sabine Le Borne
Affiliations:
Tennessee Technological University, Department of Mathematics, Box 5054 Cookeville, TN
Venue:
Computing
Year:
2003

Citing 5
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Abstract

Hierarchical matrices provide a technique for the sparse approximation and matrix arithmetic of large, fully populated matrices. This technique has been proven to be applicable to matrices arising in the boundary and finite element method for uniformly elliptic operators with L∞-coefficients. This paper analyses the application of hierarchical matrices to the convection-dominant convection-diffusion equation with constant convection. In the case of increasing convection, the convergence of a standard H-matrix approximant towards the original matrix will deteriorate. We derive a modified partitioning and admissibility condition that ensures good convergence also for the singularly perturbed case.