Asymptotic Mesh Independence of Newton-Galerkin Methods via a Refined Mysovskii Theorem.
Please always quote using this URN: urn:nbn:de:0297-zib-379
- The paper presents a theoretical characterization of the often observed asymptotic mesh independence of Newton's method, which means that Newton's method applied to discretized operator equations behaves essentially the same for all sufficiently fine discretizations. The theory does not need any uniform Lipschitz assumptions that were necessary in comparable earlier treatments. The refined Newton-Mysovskii theorem, which will be of interest in a wider context, gives both existence and uniqueness of the solution and quadratic convergence for sufficiently good starting points. Attention is restricted to Galerkin approximations even though similar results should hold for finite difference methods - but corresponding proofs would certainly be more technical. As an illustrative example, adaptive 1-D collocation methods are discussed.
| Author: | Peter Deuflhard, Florian Potra |
|---|---|
| Document Type: | ZIB-Report |
| Date of first Publication: | 1990/09/14 |
| Series (Serial Number): | ZIB-Report (SC-90-09) |
| ZIB-Reportnumber: | SC-90-09 |
| Published in: | Appeared in: SIAM J. Numer. Anal. Vol. 29, pp. 1395-1412, (1992) |
