Optimal Petrov—Galerkin Methods through Approximate Symmetrization

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Abstract
A technique of approximate symmetrization is used to derive a test space from a given trial space for a Petrov—Galerkin method. This is applied to one-dimensional diffusion—convection problems to give approximations which are near optimal in an energy norm. Rigorous and precise error bounds are derived to demonstrate the uniformly good behaviour and near optimality of the procedure over all values of the mesh Péclet number.

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