A locally based construction of analysis-suitable G^1 multi-patch spline surfaces
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Analysis-suitable G^1 (AS-G^1) multi-patch spline surfaces [4] are particular G^1-smooth multi-patch spline surfaces, which are needed to ensure the construction of C^1-smooth multi-patch spline spaces with optimal polynomial reproduction properties [16]. We present a novel local approach for the design of AS-G^1 multi-patch spline surfaces, which is based on the use of Lagrange multipliers. The presented method is simple and generates an AS-G^1 multi-patch spline surface by approximating a given G^1-smooth but non-AS-G^1 multi-patch surface. Several numerical examples demonstrate the potential of the proposed technique for the construction of AS-G^1 multi-patch spline surfaces and show that these surfaces are especially suited for applications in isogeometric analysis by solving the biharmonic problem, a particular fourth order partial differential equation, over them.
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