Internal finite element approximations in the dual variational method for second order elliptic problems with curved boundaries. (English) Zbl 0543.65074

Hlaváček, Ivan; Křížek, Michal

Apl. Mat. 29, 52-69 (1984).

Author’s summary: 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 integral 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.

Reviewer: D.R.Westbrook

MSC:

65N30	Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35J25	Boundary value problems for second-order elliptic equations

Keywords:

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

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