The /^-operator and the Galerkin Method for Strongly Elliptic Equations on Smooth Curves: Local Estimates
نویسنده
چکیده
Superconvergence in the L2-norm for the Galerkin approximation of the integral equation Lu = f is studied, where I is a strongly elliptic pseudodifferential operator on a smooth, closed or open curve. Let Uf, be the Galerkin approximation to u . By using the ^-operator, an operator that averages the values of uh , we will construct a better approximation than uh itself. That better approximation is a legacy of the highest order of convergence in negative norms. For Symm's equation on a slit the same order of convergence can be recovered if the mesh is suitably graded.
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