Discretization error estimates for discontinuous Galerkin isogeometric analysis

Abstract

Isogeometric analysis is a spline-based discretization method to partial differential equations which show the approximation power of a high-order method. The number of degrees of freedom, however, is as small as the number of degrees of freedom of a low-order method. This does not come for free as the original formulation of isogeometric analysis requires a global geometry function. Since this is too restrictive for many kinds of applications, the domain is usually decomposed into patches, where each patch is parameterized with its own geometry function. In simpler cases, the patches can be combined in a conforming way. However, for non-matching discretizations or for varying coefficients, a non-conforming discretization is desired. An symmetric interior penalty discontinuous Galerkin method for isogeometric analysis has been previously introduced. In the present paper, we give error estimates that are explicit in the spline degree. This opens the door towards the construction and the analysis of fast linear solvers, particularly multigrid solvers for non-conforming multipatch isogeometric analysis.

Keywords:

• Isogeometric analysis
• multipatch domains
• symmetric interior penalty
• discontinuous Galerkin

2010 Mathematics Subject Classifications:

• 65N15
• 41A15

Disclosure statement

No potential conflict of interest was reported by the author.

Additional information

Funding

The author was supported by the Austrian Science Fund (FWF) [S117 and P31048] and by the bilateral project DNTS-Austria 01/3/2017 (WTZ BG 03/2017), funded by Bulgarian National Science Fund and OeAD-GmbH (Austria).