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Reproducing kernel element method. IV: Globally compatible \(C^n\) (\(n\geqslant 1\)) triangular hierarchy. (English) Zbl 1093.74064
Summary: In this part of the work [for part III see the authors and J. Cao, ibid. 193, No. 12–14, 989–1011 (2004; Zbl 1060.74671)] a globally compatible \(C^n(\Omega)\) triangular element hierarchy is constructed in the framework of reproducing kernel element method (RKEM) for arbitrary two-dimensional domains. In principle, the smoothness of the globally conforming element can be made arbitrarily high (\(n \geq 1\)). The triangle interpolation field can interpolate the derivatives of an unknown function up to arbitrary \(m\)th order, (\(I^m\)), and it can reproduce complete \(k\)th order polynomials with \(k \geq m\). This is the first interpolation hierarchical structure that has ever been constructed with both minimal degrees of freedom and higher-order smoothness and continuity over discretizations of a multiple dimensional domain. The performance of the newly constructed compatible element is evaluated in solving several Kirchhoff plate problems.

MSC:
74S30 Other numerical methods in solid mechanics (MSC2010)
74S05 Finite element methods applied to problems in solid mechanics
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