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Isogeometric Analysis is a spline-based discretization method to partialdifferential equations which shows the approximation power of a high-ordermethod. The number of degrees of freedom, however, is as small as the number ofdegrees of freedom of a low-order method. This does not come for free as theoriginal formulation of Isogeometric Analysis requires a global geometryfunction. Since this is too restrictive for many kinds of applications, thedomain is usually decomposed into patches, where each patch is parameterizedwith its own geometry function. In simpler cases, the patches can be combinedin a conforming way. However, for non-matching discretizations or for varyingcoefficients, a non-conforming discretization is desired. An symmetric interiorpenalty discontinuous Galerkin (SIPG) method for Isogeometric Analysis has beenpreviously introduced. In the present paper, we give error estimates that onlydepend poly-logarithmically on the spline degree. This opens the door towardsthe construction and the analysis of fast linear solvers, particularlymultigrid solvers for non-conforming multipatch Isogeometric Analysis.

A quasi-robust discretization error estimate for discontinuous Galerkin Isogeometric Analysis