Abstract
We continue the study of the interpolation properties of the conforming finite element subspaces introduced in Chapter 18. These spaces are defined from a broken finite element space by requiring that some jumps across the mesh interfaces are zero. The cornerstone of the present construction, which is presented in a unified way, is a connectivity array with ad hoc clustering properties of the local degrees of freedom. In the present chapter, we postulate the existence of the connectivity array and show how it allows us to build global shape functions and a global interpolation operator in the conforming finite element space. The actual construction of this mapping is done in Chapters 20 and 21. We assume that the mesh is matching for simplicity.
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Ern, A., Guermond, JL. (2021). Main properties of the conforming subspaces. In: Finite Elements I. Texts in Applied Mathematics, vol 72. Springer, Cham. https://doi.org/10.1007/978-3-030-56341-7_19
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DOI: https://doi.org/10.1007/978-3-030-56341-7_19
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Publisher Name: Springer, Cham
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Online ISBN: 978-3-030-56341-7
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