Abstract
The scaled boundary finite element method (SBFEM) is a novel semi-analytical approach. The high-order completeness analysis is an important and necessary part of the basic theory of the SBFEM. Different from the standard FEM, the shape functions are constructed by the computation of the SBFEM. Thus, the key is to show that the polynomials bases can be always obtained independently of the shape of the S-elements. This paper presents the theoretical analysis of the high-order completeness of the SBFEM in mathematics for two- and three-dimensional problems, including the curved boundary elements. Moreover, in the completeness analysis, we also make up some theoretical problems and give the necessary proofs in the solving procedure of the SBFEM. Some numerical patch tests verify the theoretical results.
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