Geodesic
On a superconvergent finite element scheme for elliptic systems. II. Boundary conditions of Newton's or Neumann's type
Applications of Mathematics, Tome 32 (1987) no. 3, pp. 200-213
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A simple superconvergent scheme for the derivatives of finite element solution is presented, when linear triangular elements are employed to solve second order elliptic systems with boundary conditions of Newton's or Neumann's type. For bounded plane domains with smooth boundary the local $O(h^{3/2})$-superconvergence of the derivatives in the $L^2$-norm is proved. The paper is a direct continuations of [2], where an analogous problem with Dirichlet's boundary conditions is treated.
A simple superconvergent scheme for the derivatives of finite element solution is presented, when linear triangular elements are employed to solve second order elliptic systems with boundary conditions of Newton's or Neumann's type. For bounded plane domains with smooth boundary the local $O(h^{3/2})$-superconvergence of the derivatives in the $L^2$-norm is proved. The paper is a direct continuations of [2], where an analogous problem with Dirichlet's boundary conditions is treated.
DOI : 10.21136/AM.1987.104251
Classification : 35J25, 65N15, 65N30, 73-08, 73C99, 74S05
Keywords: finite element; triangular elements; superconvergence; post-processing; averaged gradient; elliptic systems 
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     title = {On a superconvergent finite element scheme for elliptic systems. {II.} {Boundary} conditions of {Newton's} or {Neumann's} type},
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Hlaváček, Ivan; Křížek, Michal. On a superconvergent finite element scheme for elliptic systems. II. Boundary conditions of Newton's or Neumann's type. Applications of Mathematics, Tome 32 (1987) no. 3, pp. 200-213. doi: 10.21136/AM.1987.104251

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

[7] M. Zlámal: Some superconvergence results in the finite element method. Mathematical Aspects of Finite Element Methods (Proc. Conf., Rome, 1975). Springer-Verlag, Berlin, Heidelberg, New York, 1977, 353-362. | MR

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