- Adaptive Frame Methods for Elliptic Operator Equations: The Steepest Descent Approach
- IMA Journal of Numerical Analysis
- Pages (from-to)
- Document type
- Faculty of Science (FNWI)
- Korteweg-de Vries Institute for Mathematics (KdVI)
This paper is concerned with the development of adaptive numerical methods for elliptic operator equations. We are particularly interested in discretization schemes based on wavelet frames. We show that by using three basic subroutines an implementable, convergent scheme can be derived, which, moreover, has optimal computational complexity. The scheme is based on adaptive steepest descent iterations. We illustrate our findings by numerical results for the computation of solutions of the Poisson equation with limited Sobolev smoothness on intervals in 1D and L-shaped domains in 2D.
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