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dual variational methods; stream function; finite element; piecewise smooth boundary; dual problem; optimal rate of convergence
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.
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