Local lagrange interpolation with cubic splines on tetrahedral partitions |
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Authors: | Gero Hecklin Günther Nürnberger Larry L Schumaker Frank Zeilfelder |
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Institution: | aInstitute for Mathematics, University of Mannheim, 68 131 Mannheim, Germany;bDepartment of Mathematics, Vanderbilt University, Nashville, TN 37240, USA |
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Abstract: | We describe an algorithm for constructing a Lagrange interpolation pair based on C1 cubic splines defined on tetrahedral partitions. In particular, given a set of points , we construct a set P containing and a spline space based on a tetrahedral partition whose set of vertices include such that interpolation at the points of P is well-defined and unique. Earlier results are extended in two ways: (1) here we allow arbitrary sets , and (2) the method provides optimal approximation order of smooth functions. |
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Keywords: | Trivariate splines Lagrange interpolation |
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