Volume: 21, Issue: 9(2011)
pp. 1933-1959 DOI: 10.1142/S021820251100560X
|
|
Abstract |
Full Text (PDF, 377KB)
|
References
|
 |
| Title: |
PSEUDODIFFERENTIAL EQUATIONS ON THE SPHERE WITH SPHERICAL SPLINES |
| Author(s): |
T. D. PHAM
School of Mathematics and Statistics, University of New South Wales, Sydney 2052, AustraliaT. TRAN
School of Mathematics and Statistics, University of New South Wales, Sydney 2052, AustraliaA. CHERNOV
Hausdorff Center for Mathematics, Universität Bonn, Endenicher Allee 60, 53155 Bonn, Germany
|
| History: |
Received 29 January 2010
Revised 20 January 2011
|
| Abstract: |
Spherical splines are used to define approximate solutions to strongly elliptic pseudodifferential equations on the unit sphere. These equations arise from geodesy. The approximate solutions are found by using Galerkin method. We prove optimal convergence (in Sobolev norms) of the approximate solution by spherical splines to the exact solution. Our numerical results underlie the theoretical result. |
| Keywords: |
Pseudodifferential equation; sphere; spherical spline
AMSC numbers:
65N30, 65N38, 65N15
|
|
|
