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Nonhomogeneous boundary conditions and curved triangular finite elements. (English) Zbl 0475.65073

##### MSC:
 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs 35J40 Boundary value problems for higher-order elliptic equations 35J25 Boundary value problems for second-order elliptic equations
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##### References:
 [1] J. J. Blair: Higher order approximations to the boundary conditions for the finite element method. Math. Comp. 30 (1976), 250-262. · Zbl 0342.65068 [2] J. H. Bramble S. R. Hilbert: Estimation of linear functionals on Sobolev spaces with applications to Fourier transforms and spline interpolation. SIAM J. Numer. Anal. 7 (1970), 112-124. · Zbl 0201.07803 [3] P. G. Ciarlet P. A. Raviart: The combined effect of curved boundaries and numerical integration in isoparametric finite element methods. The Mathematical Foundations of the Finite Element Method with Applications to Partial Differential Equations (A. K. Aziz, Editor), pp. 409-474, Academic Press, New York 1972. · Zbl 0262.65070 [4] P. G. Ciarlet: The Finite Element Method for Elliptic Problems. North-Holland, Amsterdam 1978. · Zbl 0383.65058 [5] S. Koukal: Piecewise polynomial interpolations in the finite element method. Apl. Mat. 18 (1973), 146-160. · Zbl 0305.65070 [6] L. Mansfield: Approximation of the boundary in the finite element solution of fourth order problems. SIAM J. Numer. Anal. 15 (1978), 568-579. · Zbl 0391.65047 [7] J. Nečas: Les méthodes directes en théorie des équations elliptiques. Academia, Prague 1967. · Zbl 1225.35003 [8] R. Scott: Interpolated boundary conditions in the finite element method. SIAM J. Numer. Anal. 12 (1975), 404-427. · Zbl 0357.65082 [9] G. Strang: Approximation in the finite element method. Numer. Math. 19 (1972), 81-98. · Zbl 0221.65174 [10] M. Zlámal: Curved elements in the finite element method. I. SIAM J. Numer. Anal. 10 (1973), 229-240. · Zbl 0285.65067 [11] M. Zlámal: Curved elements in the finite element method. II. SIAM J. Numer. Anal. 11 (1974), 347-362. · Zbl 0277.65064 [12] A. Ženíšek: Curved triangular finite $$C^m$$-elements. Apl. Mat. 23 (1978), 346-377. · Zbl 0404.35041 [13] A. Ženíšek: Discrete forms of Friedrichs’ inequalities in the finite element method. · Zbl 0475.65072
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