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Numerical solutions for second-kind Volterra integral equations by Galerkin methods. (English) Zbl 1058.65148

The authors consider a nonlinear Volterra integral equation of the second kind in the interval [0,1]. They prove that a simple interpolated finite element Galerkin scheme produces a global superconvergence in the \(L^{\infty}\)-norm. A local superconvergence of iterated finite element solutions is investigated, as well. As a by-product, an a posteriori error estimator is obtained.

MSC:

65R20 Numerical methods for integral equations
45L05 Theoretical approximation of solutions to integral equations
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
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