Abstract
Given a variational formulation of the two-dimensional Poisson problem, the present paper studies the error in approximating the exact solution via the finite element method baised upon linear elements. Using K-functional techniques, a direct sup-norm estimate in terms of a modulus of continuity of the exact solution follows directly from a well-known Jackson-type result. Because of the singularity of the Green's function associated the error bound contains a typical logarithm factor. Indeed, R. Haverkamp (1984) hats shown that this log-factor is necessary. His proof employs properties of the discrete Green's function for a related five point difference discretization. We adopt this method to establish the pointwise sharpness of the intermediate error estimate on a dense set in connection with general Lipschitz classes. The basic tool additionally used is a quantitative extension of the uniform boundedness principle. Mathematics Subject Classifications 1991: 41A25, 65N15, 65N30
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