An optimal adaptive wavelet method for nonsymmetric and indefinite elliptic problems

Authors:
Tsogtgerel Gantumur
Affiliations:
Department of Mathematics, Utrecht University, P.O. Box 80.010, NL-3508 TA Utrecht, The Netherlands
Venue:
Journal of Computational and Applied Mathematics
Year:
2008

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Abstract

In this paper, we modify the adaptive wavelet algorithm from Gantumur et al. [An optimal adaptive wavelet method without coarsening of the iterands, Technical Report 1325, Department of Mathematics, Utrecht University, March 2005, Math. Comp., to appear] so that it applies directly, i.e., without forming the normal equation, not only to self-adjoint elliptic operators but also to operators of the form L=A+B, where A is self-adjoint elliptic and B is compact, assuming that the resulting operator equation is well posed. We show that the algorithm has optimal computational complexity.