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


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
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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
[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
[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
[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
[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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.