Geodesic
Penalty method and extrapolation for axisymmetric elliptic problems with Dirichlet boundary conditions
Applications of Mathematics, Tome 35 (1990) no. 5, pp. 405-417
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A second order elliptic problem with axisymmetric data is solved in a finite element space, constructed on a triangulation with curved triangles, in such a way, that the (nonhomogeneous) boundary condition is fulfilled in the sense of a penalty. On the basis of two approximate solutions, extrapolates for both the solution and the boundary flux are defined. Some a priori error estimates are derived, provided the exact solution is regular enough. The paper extends some of the results of J.T. King [6], [7].
A second order elliptic problem with axisymmetric data is solved in a finite element space, constructed on a triangulation with curved triangles, in such a way, that the (nonhomogeneous) boundary condition is fulfilled in the sense of a penalty. On the basis of two approximate solutions, extrapolates for both the solution and the boundary flux are defined. Some a priori error estimates are derived, provided the exact solution is regular enough. The paper extends some of the results of J.T. King [6], [7].
DOI : 10.21136/AM.1990.104420
Classification : 35J25, 65N15, 65N30, 73K25
Keywords: finite elements; penalty method; axisymmetric problems; extrapolation; a priori error estimates 
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     title = {Penalty method and extrapolation for axisymmetric elliptic problems with {Dirichlet} boundary conditions},
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Hlaváček, Ivan. Penalty method and extrapolation for axisymmetric elliptic problems with Dirichlet boundary conditions. Applications of Mathematics, Tome 35 (1990) no. 5, pp. 405-417. doi: 10.21136/AM.1990.104420

[1] I. Babuška: The finite element method with penalty. Math. Соmр. 27, (1973), 221 - 228. | MR

[2] J. H. Bramble V. Thomée: Semidiscrete-least squares methods for a parabolic boundary value problem. Math. Соmр. 26 (1972), 633-648. | MR

[3] E.J.Haug K. Choi V. Komkov: Design sensitivity analysis of structural systems. Academic Press, London 1986. | MR

[4] I. Hlaváček M. Křížek: Dual finite element analysis of 3D-axisymmetric elliptic problems. (To appear).

[5] I. Hlaváček: Domain optimization in axisymmetric elliptic boundary value problems by finite elements. Apl. Mat. 33 (1988), 213-244. | MR

[6] J. T. King: New error bounds for the penalty method and extrapolation. Numer. Math. 23, (1974), 153-165. | DOI | MR | Zbl

[7] J. T. King S. M. Serbin: Boundary flux estimates for elliptic problems by the perturbed variational method. Computing 16 (1976), 339-347. | DOI | MR

[8] J. Nečas: Les methodes directes en théorie des équations elliptiques. Academia, Prague, 1967. | MR

[9] B. Mercier G. Raugel: Resolution d'un problème aux limites dans un ouvert axisymétrique par éléments finis en r, z et séries de Fourier en $\theta$. RAIRO, Anal. numér. 16 (1982), 405-461. | DOI | MR

[10] M. Zlámal: Curved elements in the finite element method. SfAM Numer. Anal. 10, (1973), 229-240. | DOI | MR

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