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Curved triangular finite \(C^ m\)-elements. (English) Zbl 0404.35041


MSC:

35J40 Boundary value problems for higher-order elliptic equations
65M99 Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems
65N99 Numerical methods for partial differential equations, boundary value problems
35A35 Theoretical approximation in context of PDEs
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
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References:

[1] Bramble J. H., Zlámal M.: Triangular elements in the finite element method. Math. Comp. 24 (1970), 809-820. · Zbl 0226.65073
[2] Ciarlet P. G., Raviart P. A.: 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
[3] Ciarlet P. G.: Numerical Analysis of the Finite Element Method. Université de Montréal, 1975.
[4] Holuša L., Kratochvíl J., Zlámal M., Ženíšek A.: The Finite Element Method. Technical Report. Computing Center of the Technical University of Brno, 1970.
[5] Kratochvíl J., Ženíšek A., Zlámal M.: A simple algorithm for the stiffness matrix of triangular plate bending finite elements. Int. J. numer. Meth. Engng. 3 (1971), 553 - 563. · Zbl 0248.73029
[6] Mansfield L.: Approximation of the boundary in the finite element solution of fourth order problems. SIAM J. Numer. Anal. 15 (1978), the June issue. · Zbl 0391.65047
[7] Nečas J.: Les méthodes directes en théorie des équations elliptiques. Academia, Prague, 1967. · Zbl 1225.35003
[8] Stroud A. H.: Approximate Calculation of Multiple Integrals. Prentice-Hall., Englewood Cliffs, N. J., 1971. · Zbl 0379.65013
[9] Zlámal M.: The finite element method in domains with curved boundaries. Int. J. numer. Meth. Engng. 5 (1973), 367-373. · Zbl 0254.65073
[10] Zlámal M.: Curved elements in the finite element method. I. SIAM J. Numer. Anal. 10(1973), 229-240. · Zbl 0285.65067
[11] Zlámal M.: Curved elements in the finite element method. II. SlAM J. Numer. Anal. 1.1 (1974), 347-362. · Zbl 0277.65064
[12] Ženíšek A.: Interpolation polynomials on the triangle. Numer. Math. 15 (1970), 283 - 296. · Zbl 0216.38901
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