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How to compute the length of a geodesic on a Riemannian manifold with small error in arbitrary Sobolev norms

Please always quote using this URN:urn:nbn:de:0296-matheon-5693
  • We compute the length of geodesics on a Riemannian manifold by regular polynomial interpolation of the global solution of the eikonal equation related to the line element $ds^2=g_ijdx^idx^j$ of the manifold. Our algorithm approximates the length functional in arbitrarily strong Sobolev norms. Error estimates are obtained where the geometric information is used. It is pointed out how the algorithm can be used to get accurate approximations of solutions of linear parabolic partial differential equations leading to obvious applications in finance, physics and other sciences.

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Metadaten
Author:Joerg Kampen
URN:urn:nbn:de:0296-matheon-5693
Referee:Dirk Becherer
Document Type:Preprint, Research Center Matheon
Language:English
Date of first Publication:2009/02/25
Release Date:2009/02/24
Tag:
Institute:Weierstraß-Institut für Angewandte Analysis und Stochastik (WIAS)
MSC-Classification:35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Fxx General first-order equations and systems / 35F20 Nonlinear first-order equations
35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Kxx Parabolic equations and systems [See also 35Bxx, 35Dxx, 35R30, 35R35, 58J35] / 35K10 Second-order parabolic equations
65-XX NUMERICAL ANALYSIS / 65Nxx Partial differential equations, boundary value problems / 65N99 None of the above, but in this section
Preprint Number:561
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