Geodesic
On semiregular families of triangulations and linear interpolation
Applications of Mathematics, Tome 36 (1991) no. 3, pp. 223-232

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MR Zbl
We consider triangulations formed by triangular elements. For the standard linear interpolation operator $\pi__h$ we prove the interpolation order to be $\left\|v-{\pi__h} v\right\|_{1,p}\leq Ch\left|v\right|_{2,p}$ for $p>1$ provided the corresponding family of triangulations is only semiregular. In such a case the well-known Zlámal's condition upon the minimum angle need not be satisfied.
We consider triangulations formed by triangular elements. For the standard linear interpolation operator $\pi__h$ we prove the interpolation order to be $\left\|v-{\pi__h} v\right\|_{1,p}\leq Ch\left|v\right|_{2,p}$ for $p>1$ provided the corresponding family of triangulations is only semiregular. In such a case the well-known Zlámal's condition upon the minimum angle need not be satisfied.
DOI : 10.21136/AM.1991.104461
Classification : 41A05, 65D05, 65N30
Keywords: finite elements; linear interpolation; maximum angle condition; Zlámal’s condition 
Křížek, Michal. On semiregular families of triangulations and linear interpolation. Applications of Mathematics, Tome 36 (1991) no. 3, pp. 223-232. doi: 10.21136/AM.1991.104461
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