On semiregular families of triangulations and linear interpolation
Applications of Mathematics (1991)
- Volume: 36, Issue: 3, page 223-232
- ISSN: 0862-7940
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topKřížek, Michal. "On semiregular families of triangulations and linear interpolation." Applications of Mathematics 36.3 (1991): 223-232. <http://eudml.org/doc/15675>.
@article{Křížek1991,
abstract = {We consider triangulations formed by triangular elements. For the standard linear interpolation operator $\pi __h$ we prove the interpolation order to be $\left\Vert v-\{\pi __h\} v\right\Vert _\{1,p\}\le Ch\left|v\right|_\{2,p\}$ 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.},
author = {Křížek, Michal},
journal = {Applications of Mathematics},
keywords = {finite elements; linear interpolation; maximum angle condition; Zlámal’s condition; Zlámal’s condition},
language = {eng},
number = {3},
pages = {223-232},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On semiregular families of triangulations and linear interpolation},
url = {http://eudml.org/doc/15675},
volume = {36},
year = {1991},
}
TY - JOUR
AU - Křížek, Michal
TI - On semiregular families of triangulations and linear interpolation
JO - Applications of Mathematics
PY - 1991
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 36
IS - 3
SP - 223
EP - 232
AB - We consider triangulations formed by triangular elements. For the standard linear interpolation operator $\pi __h$ we prove the interpolation order to be $\left\Vert v-{\pi __h} v\right\Vert _{1,p}\le Ch\left|v\right|_{2,p}$ 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.
LA - eng
KW - finite elements; linear interpolation; maximum angle condition; Zlámal’s condition; Zlámal’s condition
UR - http://eudml.org/doc/15675
ER -
References
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- Mingxia Li, Shipeng Mao, Anisotropic interpolation error estimates via orthogonal expansions
- Aleš Prachař, On discontinuous Galerkin method and semiregular family of triangulations
- Alexander Ženíšek, Finite element variational crimes in the case of semiregular elements
- Alexander Ženíšek, Jana Hoderová-Zlámalová, Semiregular hermite tetrahedral finite elements
- Peter Oswald, Divergence of FEM: Babuška-Aziz triangulations revisited
- Zdeněk Milka, Finite element solution of a stationary heat conduction equation with the radiation boundary condition
- Jana Zlámalová, Semiregular finite elements in solving some nonlinear problems
- Kenta Kobayashi, Takuya Tsuchiya, Error estimation for finite element solutions on meshes that contain thin elements
- Kenta Kobayashi, Takuya Tsuchiya, A priori error estimates for Lagrange interpolation on triangles
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