Wavelet Least Square Methods for Boundary Value Problems
نویسندگان
چکیده
This paper is concerned with least squares methods for the numerical solution of operator equations. Our primary focus is the discussion of the following conceptual issues: the selection of appropriate least squares functionals, their numerical evaluation in the special light of recent developments of multiscale and wavelet methods and a natural way of preconditioning the resulting systems of linear equations. To bring out the essential driving mechanisms, we formulate rst the problem in a possibly general setting. We will then identify several special cases that t into this framework such as second order elliptic boundary value problems, their formulation as a rst order system, transmission problems, the system of Stokes equations or more general saddle point problems. Particular emphasis is placed on the separate treatment of essential non-homogeneous boundary conditions. One primary motivation has been the well-known fact that a major obstacle in the context of least{square methods is the evaluation of certain norms such as the H ?1 {norm. In particular, we exploit in this regard the fact that weighted sequence norms of wavelet coeecients are equivalent to relevant function norms arising in the least squares context for various important applications.
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تاریخ انتشار 1999