Explicit error estimates for spline approximation of arbitrary smoothness in isogeometric analysis

09/08/2019

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by   Espen Sande, et al.

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In a recent publication, explicit constants have been provided in a priori error estimates for approximation with spline spaces of maximal smoothness defined on arbitrary grids. In this paper, we consider the general case of approximation with spline spaces of arbitrary smoothness defined on arbitrary grids, and provide explicit constants in a priori error estimates for both the L^2-projection and the Ritz projection. We begin with presenting results for univariate spline spaces, and then we address multivariate tensor-product spline spaces and isogeometric spline spaces generated by means of a mapped geometry, both in the single-patch and in the multi-patch case.