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Convergence in discrete Cauchy problems and applications to circle patterns
Author(s):
D.
Matthes
Journal:
Conform. Geom. Dyn.
9
(2005),
1-23.
MSC (2000):
Primary 30G25;
Secondary 35A10, 52C15
Posted:
February 9, 2005
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Abstract:
A lattice-discretization of analytic Cauchy problems in two dimensions is presented. It is proven that the discrete solutions converge to a smooth solution of the original problem as the mesh size  tends to zero. The convergence is in  and the approximation error for arbitrary derivatives is quadratic in  . In application,  -approximation of conformal maps by Schramm's orthogonal circle patterns and lattices of cross-ratio minus one is shown.
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Additional Information:
D.
Matthes
Affiliation:
Institut für Mathematik, Technische Universität Berlin, Straße des 17.Juni 136, 10623 Berlin, Germany
Address at time of publication:
Institut für Mathematik, Johannes Gutenberg Universität Mainz, Staudingerweg 9, 55128 Mainz, Germany
Email:
matthes@mathematik.uni-mainz.de
DOI:
10.1090/S1088-4173-05-00118-9
PII:
S 1088-4173(05)00118-9
Received by editor(s):
March 19, 2004
Received by editor(s) in revised form:
November 16, 2004
Posted:
February 9, 2005
Additional Notes:
Supported by the SFB 288 ``Differential Geometry and Quantum Physics'' of the Deutsche Forschungsgemeinschaft
Copyright of article:
Copyright
2005,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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