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- W4200244989 abstract "In this article, the construction of versatile transition elements for applications in dynamics is comprehensively discussed. Based on the transfinite mapping technique, also known as Coons–Gordon interpolation, piece-wise shape functions are derived such that an arbitrary number of elements with different ansatz spaces is coupled conformingly. This is an important prerequisite to enable the use of local mesh refinement strategies for regular quadrilateral discretizations. Due to the special construction of the shape functions, there are no hanging nodes that need to be taken care of. The focus in this contribution is on dynamics, and therefore, Lagrange polynomials are taken as the basis to construct shape functions for arbitrary transition elements. As a consequence, the Kronecker-delta and partition of unity properties are recovered. These properties are crucial to diagonalize the mass matrix using standard mass lumping techniques such as row-summing and diagonal scaling. The performance of the proposed family of elements is assessed by means of several benchmark examples, where the numerical rates of convergence are determined for both consistent and lumped mass matrix formulations." @default.
- W4200244989 created "2021-12-31" @default.
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- W4200244989 date "2021-12-01" @default.
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- W4200244989 title "High order transition elements: The xy-element concept, Part II: Dynamics" @default.
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- W4200244989 doi "https://doi.org/10.1016/j.cma.2021.114145" @default.
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