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On the super-approximation property of Galerkin’s method with finite elements. (English) Zbl 0745.65064

Author’s summary: For Galerkin’s method with finite elements as trial functions for strongly elliptic operator equations in the Hilbert scale \(H^ t\) the superapproximation property and the optimal convergence rate are obtained by using the Aubin-Nitsche lemma. This applies in particular to spline collocation methods for a wide class of pseudo-differential equations.

MSC:

65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N35 Spectral, collocation and related methods for boundary value problems involving PDEs
35J25 Boundary value problems for second-order elliptic equations
35S15 Boundary value problems for PDEs with pseudodifferential operators
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References:

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