Article
Full entry |
PDF
(1.6 MB)
Feedback
PDF
(1.6 MB)
Feedback
Keywords:
finite element method; simplicial isoparametric elements; Friedrichs’ inequality
finite element method; simplicial isoparametric elements; Friedrichs’ inequality
Summary:
The proof of the Friedrichs' inequality on the class of finite dimensional spaces used in the finite element method is given. In particular, the approximate spaces generated by simplicial isoparametric elements are considered.
References:
[1] P. G. Ciarlet P. A. Raviart: The combined effect of curved boundaries and numerical integration in isoparametric finite element methods. In: The Mathematical Foundations of the Finite Element Method with Applications to Partial Differential Equations (A. K. Aziz Editor). Academic Press. New York and London. 1972. MR 0421108
[2] L. Čermák: The finite element solution of second order elliptic problems with the Newton boundary condition. Apl. Mat., 28 (1983), 430-456. MR 0723203
[3] J. Nečas: Les méthodes directes en théorie des équations elliptiques. Academia. Prague. 1967. MR 0227584
[4] K. Yosida: Functional Analysis. Springer-Verlag. Berlin-Heidelberg-New York. 1966.
[5] A. Ženíšek: Nonhomogeneous boundary conditions and curved triangular finite elements. Apl. Mat., 26 (1981), 121-141. MR 0612669
[6] A. Ženíšek: Discrete forms of Friedrichs' inequalities in the finite element method. R.A.LR.O Numer. Anal., 15 (1981), 265-286. MR 0631681 | Zbl 0475.65072
Search
Partner of
