The sharpness condition for constructing a finite element from a superspline

2024/07/04 by Jun Hu, Ting Lin, Hu, Jun +5
Engineering · Agricultural and Biological Sciences · #Advanced Theoretical and Applied Studies in Material Sciences and Geometry #Advanced Numerical Analysis Techniques #Engineering and Agricultural Innovations

paper · pdf · doi:10.48550/arxiv.2407.03680

Abstract

This paper addresses sharpness conditions for constructing C^r conforming finite element spaces from a superspline spaces on general simplicial triangulations. We introduce the concept of extendability for the pre-element spaces, which encompasses both the superspline spaces and the finite element spaces. By examining the extendability condition for both types of spaces, we provide an answer to the conditions regarding the construction. A corollary of our results is that constructing C^r conforming elements in d dimensions generally requires an extra C^2^sr continuity on s-codimensional simplices, and the polynomial degree is at least (2^d r + 1).

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