Document Zbl 0475.65072

Discrete forms of Friedrichs’ inequalities in the finite element method. (English) Zbl 0475.65072

RAIRO, Anal. Numér. 15, 265-286 (1981).

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MSC:

65N30	Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
74K20	Plates
74S05	Finite element methods applied to problems in solid mechanics
35J40	Boundary value problems for higher-order elliptic equations

Keywords:

discrete forms of Friedrichs’ inequalities; finite element method; curved finite elements; bending of thin elastic plates

Citations:

Zbl 0262.65070; Zbl 0383.65058

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Full Text: DOI EuDML

References:

[1]	J. H. BRAMBLE, M. ZLÄMAL, Triangular elements in the finite element method, Math. Comp. 24(1970), 809-820. Zbl0226.65073 MR282540 · Zbl 0226.65073 · doi:10.2307/2004615
[2]	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 Diffe-rential Equations (A. K. Aziz, Editor), Academic Press, New York, 1972, pp. 409-474. Zbl0262.65070 MR421108 · Zbl 0262.65070
[3]	P. G. CIARLET, The Finite Element Method for Elliptic Problems. North-Holland, Amsterdam, 1978. Zbl0383.65058 MR520174 · Zbl 0383.65058
[4]	J. HREBICEK, A numerical analysis of a general biharmonic problem by the finite element method. (To appear.) Zbl0541.65072 · Zbl 0541.65072
[5]	L MANSFIELD, Approximation of the boundary in the finite element solution of fourth order problems SIAM J Numer Anal 15 (1978), 568-579 Zbl0391.65047 MR471373 · Zbl 0391.65047 · doi:10.1137/0715037
[6]	J NECAS, Les méthodes directes en théorie des équations elliptiques Academia, Prague, 1967 Zbl1225.35003 MR227584 · Zbl 1225.35003
[7]	M ZLAMAL, Curved elements in the finite element method I SIAM J Numer Anal 10 (1973), 229-240 Zbl0285.65067 MR395263 · Zbl 0285.65067 · doi:10.1137/0710022
[8]	M ZLAMAL, Curved elements in the finite element method II SIAM J Numer Anal 11 (1974), 347-362 Zbl0277.65064 MR343660 · Zbl 0277.65064 · doi:10.1137/0711031
[9]	[9] A ZENISEK, Curved triangular finite C m -elements Apl Mat 23 (1978), 346-377 Zbl0404.35041 MR502072 · Zbl 0404.35041
[10]	[10] A ZENISEK, Nonhomogeneous boundary conditions and curved triangular finite elements Apl Mat 26(1981), 121-141 Zbl0475.65073 MR612669 · Zbl 0475.65073

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