Clement-type interpolation on spherical domains--interpolation error estimates and application to a posteriori error estimation

T. Apel
2005 IMA Journal of Numerical Analysis  
In this paper, a mixed boundary value problem for the Laplace-Beltrami operator is considered for spherical domains in IR 3 , i.e. for domains on the unit sphere. These domains are parametrized by spherical coordinates (ϕ, θ), such that functions on the unit sphere are considered as functions in these coordinates. Careful investigation leads to the introduction of a proper finite element space corresponding to an isotropic triangulation of the underlying domain on the unit sphere. Error
more » ... s are proven for a Clémenttype interpolation operator, where appropriate, weighted norms are used. The estimates are applied to the deduction of a reliable and efficient residual error estimator for the Laplace-Beltrami operator.
doi:10.1093/imanum/drh024 fatcat:ivf3xu742jdvvgnpx3p7si54me