Abstract
In this work, arbitrarily smooth, globally compatible, I m/C n/P k interpolation hierarchies are constructed in the framework of reproducing kernel element method (RKEM) for multi-dimensional domains. This is the first interpolation hierarchical structure that has been ever constructed with both minimal degrees of freedom and higher order continuity and reproducing conditions over multi-dimensional domains. The proposed hierarchical structure possesses the generalized Kronecker property, i.e., ∂ α Ψ I/(β)/∂x α(x J) = δ IJ δ αβ, |α|, |β| ≤ m. The newly constructed globally conforming interpolant is a hybrid of global partition polynomials (C∞) and a smooth (C n) compactly supported meshfree partition of unity. Examples of compatible RKEM hierarchical interpolations are illustrated, and they are used in a Galerkin procedure to solve differential equations.
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Li, S., Simkins, D.C., Lu, H., Liu, W.K. (2005). Reproducing Kernel Element Interpolation: Globally Conforming I m/C n/P k Hierarchies. In: Griebel, M., Schweitzer, M.A. (eds) Meshfree Methods for Partial Differential Equations II. Lecture Notes in Computational Science and Engineering, vol 43. Springer, Berlin, Heidelberg . https://doi.org/10.1007/3-540-27099-X_7
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DOI: https://doi.org/10.1007/3-540-27099-X_7
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