A Nash-Hormander iteration and boundary elements for the Molodensky problem

作者：Costea Adrian; Gimperlein Heiko^*; Stephan Ernst P

来源：Numerische Mathematik, 2014, 127(1): 1-34.

DOI：10.1007/s00211-013-0579-8

We investigate the numerical approximation of the nonlinear Molodensky problem, which reconstructs the surface of the earth from the gravitational potential and the gravity vector. The method, based on a smoothed Nash-Hormander iteration, solves a sequence of exterior oblique Robin problems and uses a regularization based on a higher-order heat equation to overcome the loss of derivatives in the surface update. In particular, we obtain a quantitative a priori estimate for the error after m steps, justify the use of smoothing operators based on the heat equation, and comment on the accurate evaluation of the Hessian of the gravitational potential on the surface, using a representation in terms of a hypersingular integral. Aboundary element method is used to solve the exterior problem. Numerical results compare the error between the approximation and the exact solution in a model problem.

• 出版日期2014-5