# Nonhomogeneous boundary conditions and curved triangular finite elements

Aplikace matematiky (1981)

- Volume: 26, Issue: 2, page 121-141
- ISSN: 0862-7940

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topŽeníšek, Alexander. "Nonhomogeneous boundary conditions and curved triangular finite elements." Aplikace matematiky 26.2 (1981): 121-141. <http://eudml.org/doc/15188>.

@article{Ženíšek1981,

abstract = {Approximation of nonhomogeneous boundary conditions of Dirichlet and Neumann types is suggested in solving boundary value problems of elliptic equations by the finite element method. Curved triangular elements are considered. In the first part of the paper the convergence of the finite element method is analyzed in the case of nonhomogeneous Dirichlet problem for elliptic equations of order $2m+2$, in the second part of the paper in the case of nonhomogeneous mixed boundary value problem for second order elliptic equations. In both parts of the paper of numerical integration is studied.},

author = {Ženíšek, Alexander},

journal = {Aplikace matematiky},

keywords = {nonhomogeneous boundary conditions; Dirichlet; Neumann; finite element method; curved triangular elements; convergence; nonhomogeneous boundary conditions; Dirichlet; Neumann; finite element method; curved triangular elements; convergence},

language = {eng},

number = {2},

pages = {121-141},

publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},

title = {Nonhomogeneous boundary conditions and curved triangular finite elements},

url = {http://eudml.org/doc/15188},

volume = {26},

year = {1981},

}

TY - JOUR

AU - Ženíšek, Alexander

TI - Nonhomogeneous boundary conditions and curved triangular finite elements

JO - Aplikace matematiky

PY - 1981

PB - Institute of Mathematics, Academy of Sciences of the Czech Republic

VL - 26

IS - 2

SP - 121

EP - 141

AB - Approximation of nonhomogeneous boundary conditions of Dirichlet and Neumann types is suggested in solving boundary value problems of elliptic equations by the finite element method. Curved triangular elements are considered. In the first part of the paper the convergence of the finite element method is analyzed in the case of nonhomogeneous Dirichlet problem for elliptic equations of order $2m+2$, in the second part of the paper in the case of nonhomogeneous mixed boundary value problem for second order elliptic equations. In both parts of the paper of numerical integration is studied.

LA - eng

KW - nonhomogeneous boundary conditions; Dirichlet; Neumann; finite element method; curved triangular elements; convergence; nonhomogeneous boundary conditions; Dirichlet; Neumann; finite element method; curved triangular elements; convergence

UR - http://eudml.org/doc/15188

ER -

## References

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- M. Zlámal, 10.1137/0710022, SIAM J. Numer. Anal. 10 (1973), 229-240. (1973) MR0395263DOI10.1137/0710022
- M. Zlámal, 10.1137/0711031, SIAM J. Numer. Anal. 11 (1974), 347-362. (1974) MR0343660DOI10.1137/0711031
- A. Ženíšek, Curved triangular finite ${C}^{m}$-elements, Apl. Mat. 23 (1978), 346-377. (1978) Zbl0403.65045MR0502072
- A. Ženíšek, Discrete forms of Friedrichs' inequalities in the finite element method, (To appear.) Zbl0475.65072MR0631681

## Citations in EuDML Documents

top- Alexander Ženíšek, Discrete forms of Friedrichs' inequalities in the finite element method
- Libor Čermák, A note on a discrete form of Friedrichs' inequality
- Alexander Ženíšek, How to avoid the use of Green's theorem in the Ciarlet-Raviart theory of variational crimes
- Jiří Hřebíček, Numerical analysis of the general biharmonic problem by the finite element method
- Libor Čermák, The finite element solution of second order elliptic problems with the Newton boundary condition
- Miloslav Feistauer, Veronika Sobotíková, Finite element approximation of nonlinear elliptic problems with discontinuous coefficients
- Miloslav Feistauer, Karel Najzar, Karel Švadlenka, On a parabolic problem with nonlinear Newton boundary conditions

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