A Galerkin finite element method is analyzed for a class of the Fredholm type integro-differential equations. The method is applied to Pippard's nonlocal superconductivity model. Optimal H 1 norm error estimates are derived for the finite element solution of the current potential. A class of superconvergent post-processing techniques are developed to obtain more accurate approximations to the magnetic field from the finite element solutions. An H 1 semi-norm actual error indicator is derived and is used to generate an adaptive grid refinement procedure. Several numerical examples are presented.
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Lin et al. (1995) studied this question.
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