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Keywords:
finite element method; nonlinear elliptic problems; semiregular elements; maximum angle condition; effect of numerical integration; approximation of the boundary
finite element method; nonlinear elliptic problems; semiregular elements; maximum angle condition; effect of numerical integration; approximation of the boundary
Summary:
In this paper, under the maximum angle condition, the finite element method is analyzed for nonlinear elliptic variational problem formulated in [4]. In [4] the analysis was done under the minimum angle condition.
References:
[1] P. G. Ciarlet: The Finite Element Method for Elliptic Problems. North-Holland Publishing Company, Amsterdam, 1978. MR 0520174 | Zbl 0383.65058
[2] M. Feistauer, K. Najzar: Finite element approximation of a problem with a nonlinear Newton boundary condition. Numer. Math. 78 (1998), 403–425. DOI 10.1007/s002110050318 | MR 1603350
[3] M. Feistauer, V. Sobotíková: Finite element approximation of nonlinear elliptic problems with discontinuous coefficients. RAIRO Modél. Math. Anal. Numér. 24 (1990), 457–500. DOI 10.1051/m2an/1990240404571 | MR 1070966
[4] M. Feistauer, A. Ženíšek: Finite element solution of nonlinear elliptic problems. Numer. Math. 50 (1987), 451–475. MR 0875168
[5] M. Křížek: On semiregular families of triangulations and linear interpolation. Appl. Math. 36 (1991), 223–232. MR 1109126
[6] A. Kufner, O. John and S. Fučík : Function Spaces. Academia, Praha, 1977. MR 0482102
[7] J. Nečas: Les Métodes Directes en Théorie des Equations Elliptiques. Academia-Masson, Prague-Paris, 1967. MR 0227584
[8] L. A. Oganesian, L. A Rukhovec: Variational-Difference Methods for the Solution of Elliptic Problems. Izd. Akad. Nauk ArSSR, Jerevan, 1979. (Russian)
[9] A. Ženíšek: Nonlinear Elliptic and Evolution Problems and Their Finite Element Approximations. Academic Press, London, 1990. MR 1086876
[10] A. Ženíšek: The maximum angle condition in the finite element method for monotone problems with applications in magnetostatics. Numer. Math. 71 (1995), 399–417. DOI 10.1007/s002110050151 | MR 1347576
[11] A. Ženíšek: Finite element variational crimes in the case of semiregular elements. Appl. Math. 41 (1996), 367–398. MR 1404547
[12] A. Ženíšek: The use of semiregular finite elements. In: Proceedings of EQUADIFF, Conference on Differential Equations and Their Applications (R. P. Agarwal, F. Neuman and J. Vosmanský, eds.), Masaryk University, Brno & Electronic Publishing House, Stony Brook, New York, 1998, pp. 201–251.
[13] M. Zlámal: Curved elements in the finite element method I . SIAM J. Numer. Anal. 10 (1973), 229–240. DOI 10.1137/0710022 | MR 0395263
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