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A Posteriori Error Estimates for Hypersingular Integral Equation on Spheres with Spherical Splines
Duong Thanh Pham
,
Tung Le
Abstract
A posteriori residual and hierarchical upper bounds for the error estimates are proved when solving the hypersingular integral equation on the unit sphere by using the Galerkin method with spherical splines. Based on these a posteriori error estimates, adaptive mesh refining procedures are used to reduce complexity and computational cost of the discrete problems. Numerical experiments illustrate our theoretical results.