@article{Ženíšek1996,
abstract = {The finite element method for a strongly elliptic mixed boundary value problem is analyzed in the domain $\Omega $ whose boundary $\partial \Omega $ is formed by two circles $\Gamma _1$, $\Gamma _2$ with the same center $S_0$ and radii $R_1$, $R_2=R_1+\varrho $, where $\varrho \ll R_1$. On one circle the homogeneous Dirichlet boundary condition and on the other one the nonhomogeneous Neumann boundary condition are prescribed. Both possibilities for $u=0$ are considered. The standard finite elements satisfying the minimum angle condition are in this case inconvenient; thus triangles obeying only the maximum angle condition and narrow quadrilaterals are used. The restrictions of test functions on triangles are linear functions while on quadrilaterals they are four-node isoparametric functions. Both the effect of numerical integration and that of approximation of the boundary are analyzed. The rate of convergence $O(h)$ in the norm of the Sobolev space $H^1$ is proved under the following conditions: 1. the},
author = {Ženíšek, Alexander},
journal = {Applications of Mathematics},
keywords = {finite element method; elliptic problems; semiregular elements; maximum angle condition; variational crimes; finite element method; elliptic problems; maximum angle condition; variational crimes},
language = {eng},
number = {5},
pages = {367-398},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Finite element variational crimes in the case of semiregular elements},
url = {http://eudml.org/doc/32956},
volume = {41},
year = {1996},
}
TY - JOUR
AU - Ženíšek, Alexander
TI - Finite element variational crimes in the case of semiregular elements
JO - Applications of Mathematics
PY - 1996
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 41
IS - 5
SP - 367
EP - 398
AB - The finite element method for a strongly elliptic mixed boundary value problem is analyzed in the domain $\Omega $ whose boundary $\partial \Omega $ is formed by two circles $\Gamma _1$, $\Gamma _2$ with the same center $S_0$ and radii $R_1$, $R_2=R_1+\varrho $, where $\varrho \ll R_1$. On one circle the homogeneous Dirichlet boundary condition and on the other one the nonhomogeneous Neumann boundary condition are prescribed. Both possibilities for $u=0$ are considered. The standard finite elements satisfying the minimum angle condition are in this case inconvenient; thus triangles obeying only the maximum angle condition and narrow quadrilaterals are used. The restrictions of test functions on triangles are linear functions while on quadrilaterals they are four-node isoparametric functions. Both the effect of numerical integration and that of approximation of the boundary are analyzed. The rate of convergence $O(h)$ in the norm of the Sobolev space $H^1$ is proved under the following conditions: 1. the
LA - eng
KW - finite element method; elliptic problems; semiregular elements; maximum angle condition; variational crimes; finite element method; elliptic problems; maximum angle condition; variational crimes
UR - http://eudml.org/doc/32956
ER -
