Geodesic
Internal finite element approximations in the dual variational method for second order elliptic problems with curved boundaries
Applications of Mathematics, Tome 29 (1984) no. 1, pp. 52-69
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Using the stream function, some finite element subspaces of divergence-free vector functions, the normal components of which vanish on a part of the piecewise smooth boundary, are constructed. Applying these subspaces, an internal approximation of the dual problem for second order elliptic equations is defined. A convergence of this method is proved without any assumption of a regularity of the solution. For sufficiently smooth solutions an optimal rate of convergence is proved. The internal approximation can be obtained by solving a system of linear algebraic equations with a positive definite matrix.
Using the stream function, some finite element subspaces of divergence-free vector functions, the normal components of which vanish on a part of the piecewise smooth boundary, are constructed. Applying these subspaces, an internal approximation of the dual problem for second order elliptic equations is defined. A convergence of this method is proved without any assumption of a regularity of the solution. For sufficiently smooth solutions an optimal rate of convergence is proved. The internal approximation can be obtained by solving a system of linear algebraic equations with a positive definite matrix.
DOI : 10.21136/AM.1984.104068
Classification : 35J25, 65N30
Keywords: dual variational methods; stream function; finite element; piecewise smooth boundary; dual problem; optimal rate of convergence 
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Hlaváček, Ivan; Křížek, Michal. Internal finite element approximations in the dual variational method for second order elliptic problems with curved boundaries. Applications of Mathematics, Tome 29 (1984) no. 1, pp. 52-69. doi: 10.21136/AM.1984.104068

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