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viscoelastic bending; thin plates; finite elements in space; finite difference in time; rate of convergence
The present paper deals with numerical solution of a viscoelastic plate. The discrete problem is defined by $C^1$-elements and a linear multistep method. The effect of numerical integration is studied as well. The rate of cnvergence is established. Some examples are given in the conclusion.
[1] K. Bell: A refined triangular plate bending finite element. Int. J. Numer. Meth. Engng. 1 (1969), 101-122. DOI 10.1002/nme.1620010108
[2] J. H. Bramble M. Zlámal: Triangular elements in the finite element method. Math. Соmр. 24 (1970), 809-820. MR 0282540
[3] J. Brilla: Visco-elastic bending of anisotropic plates. (in Slovak), Stav. Čas. 17 (1969), 153-175.
[4] J. Brilla: Finite element method for quasiparabolic equations. in Proc. of the 4th symposium on basic problems of numer. math., Plzeň (1978), 25-36. MR 0566152 | Zbl 0445.73060
[5] P. G. Ciarlet: The Finite Element Method for Elliptic Problems. North-Holland, Amsterdam, 1978. MR 0520174 | Zbl 0383.65058
[6] V. Girault P.-A. Raviart: Finite Element Approximation of the Navier-Stokes Equations. Springer-Verlag, Berlin-Heidelberg-New York, 1979. MR 0548867
[7] J. Hřebíček: Numerical analysis of the general biharmonic problem by the finite element method. Apl. mat. 27 (1982), 352-374. MR 0674981
[8] V. Kolář J. Kratochvíl F. Leitner A. Ženíšek: Calculation of plane and Space Constructions by the Finite Element Method. (Czech). SNTL, Praha, 1979.
[9] J. Kratochvíl A. Ženíšek M. Zlámal: A simple algorithm for the stiffness matrix of triangular plate bending finite elements. Int. J. Numer. Meth. Engng. 3 (1971), 553 - 563. DOI 10.1002/nme.1620030409
[10] J. Nedoma: The finite element solution of parabolic equations. Apl. mat. 23 (1978), 408-438. MR 0508545 | Zbl 0427.65075
[11] S. Turčok: Solution of quasiparabolic differential equations by finite element method. (in Slovak), Thesis, Komenský University Bratislava, (1978).
[12] M. Zlámal: On the finite element method. Numer. Math. 12 (1968), 394 - 409. DOI 10.1007/BF02161362 | MR 0243753
[13] M. Zlámal: Finite element methods for nonlinear parabolic equations. R.A.I.R.O. Numer. Anal. 11 (1977), 93-107. MR 0502073
[14] A. Ženíšek: Curved triangular finite $C^m$-elements. Apl. Mat. 23 (1978), 346-377. MR 0502072
[15] A. Ženíšek: Discrete forms of Friedrichs' inequalities in the finite element method. R.A.I. R. O. Numer. Anal. 15 (1981), 265-286. MR 0631681 | Zbl 0475.65072
[16] A. Ženíšek: Finite element methods for coupled thermoelasticity and coupled consolidation of clay. (To appear in R.A.I.R.O. Numer. Anal. 18 (1984).) MR 0743885
[17] E. Godlewski A. Puech-Raoult: Équations d'évolution linéaires du second ordre et méthodes multipas. R.A.I.R.O. Numer. Anal. 13 (1979), 329-353. MR 0555383
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