arXiv:1910.01311 Abstract | arXiv Analytics

arXiv:1910.01311 [math.NA]Abstract References Reviews Resources

Adaptive IGAFEM with optimal convergence rates: T-splines

Published 2019-10-03Version 1

We consider an adaptive algorithm for finite element methods for the isogeometric analysis (IGAFEM) of elliptic (possibly non-symmetric) second-order partial differential equations. We employ analysis-suitable T-splines of arbitrary odd degree on T-meshes generated by the refinement strategy of [Morgenstern, Peterseim, Comput. Aided Geom. Design 34 (2015)] in 2D resp. [Morgenstern, SIAM J. Numer. Anal. 54 (2016)] in 3D. Adaptivity is driven by some weighted residual a posteriori error estimator. We prove linear convergence of the error estimator (resp. the sum of energy error plus data oscillations) with optimal algebraic rates.

Comments: arXiv admin note: text overlap with arXiv:1701.07764

Categories: math.NA, cs.NA

Keywords: optimal convergence rates, adaptive igafem, energy error plus data oscillations, error estimator, second-order partial differential equations

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