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— In the case of a rectangular domain uniform error estimâtes of optimal order are proved for Galerkin approximate solutions of a Dirichlet problem with variable coefficients. For the case of Laplacé's équation and a special choice of the Galerkin space9 convergence is shown to be faster at the knots than is possible ghbally.

An $L^\infty $ estimate and a superconvergence result for a Galerkin method for elliptic equations based on tensor products of piecewise polynomials