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- W3000210487 abstract "The paper is concerned with the space of C1 continuous polynomial splines of degree 5 on general triangulations such that the restriction to each triangle corresponds to a Bell element. It is investigated how the standard construction of Bell elements, which is based on prescribing values and derivatives up to order two at the vertices of the triangulation, can be used to define different bases. The most straightforward one is the nodal basis, which lacks stability, but it is shown that this can be improved by scaling the interpolation data. However, the prime focus of the paper is on the construction of B-spline-like bases that depend on the choice of special domain triangles associated with the vertices of the triangulation. A B-spline-like basis consists of functions that are locally supported and form a partition of unity. If the triangulation satisfies certain geometric constraints (e.g. is acute) and the domain triangles are chosen suitably, the basis is also non-negative. The stability analysis of the derived bases is addressed theoretically as well as numerically, the latter with the examples of least square fitting and PDE solving." @default.
- W3000210487 created "2020-01-23" @default.
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- W3000210487 date "2020-05-01" @default.
- W3000210487 modified "2023-09-23" @default.
- W3000210487 title "On stable representations of Bell elements" @default.
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- W3000210487 doi "https://doi.org/10.1016/j.camwa.2019.12.023" @default.
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