Geodesic
On interpolation error on degenerating prismatic elements
Applications of Mathematics, Tome 63 (2018) no. 3, pp. 237-257 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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We propose an analogue of the maximum angle condition (commonly used in finite element analysis for triangular and tetrahedral meshes) for the case of prismatic elements. Under this condition, prisms in the meshes may degenerate in certain ways, violating the so-called inscribed ball condition presented by P. G. Ciarlet (1978), but the interpolation error remains of the order $O(h)$ in the $H^{1}$-norm for sufficiently smooth functions.
We propose an analogue of the maximum angle condition (commonly used in finite element analysis for triangular and tetrahedral meshes) for the case of prismatic elements. Under this condition, prisms in the meshes may degenerate in certain ways, violating the so-called inscribed ball condition presented by P. G. Ciarlet (1978), but the interpolation error remains of the order $O(h)$ in the $H^{1}$-norm for sufficiently smooth functions.
DOI : 10.21136/AM.2018.0357-17
Classification : 65N12, 65N15, 65N30, 65N50
Keywords: prismatic finite element; interpolation error; semiregular family of prismatic partitions 
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     title = {On interpolation error on degenerating prismatic elements},
     journal = {Applications of Mathematics},
     pages = {237--257},
     year = {2018},
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Khademi, Ali; Korotov, Sergey; Vatne, Jon Eivind. On interpolation error on degenerating prismatic elements. Applications of Mathematics, Tome 63 (2018) no. 3, pp. 237-257. doi: 10.21136/AM.2018.0357-17

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