An isogeometric mortar method for the coupling of multiple NURBS domains with optimal convergence rates
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Date
2019-09
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Abstract
We investigate the mortar finite element method for second order elliptic boundary value problems on domains which are decomposed into patches Ω_k with tensor-product NURBS parameterizations. We follow the methodology of IsoGeometric Analysis (IGA) and choose discrete spaces X_h,k on each patch Ω_k as tensor-product NURBS spaces of the same or higher degree as given by the parameterization. Our work is an extension of [12] and highlights several aspects which did not receive full attention before. In particular, by choosing appropriate spaces of polynomial splines as Lagrange multipliers, we obtain a uniform infsup-inequality. Moreover, we provide a new additional condition on the discrete spaces X_h,k which is required for obtaining optimal convergence rates of the mortar method. Our numerical examples demonstrate that the optimal rate is lost if this condition is neglected.
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isogeometric analysis, infsup-stability, modified Lagrange multiplier space, coupling of non-conforming meshes, Mortar method, optimal convergence