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Internal finite element approximations in the dual variational method for second order elliptic problems with curved boundaries

Ivan Hlaváček, Michal Křížek (1984)

Aplikace matematiky

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...

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