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Ritz-Volterra projections to finite-element spaces and applications to integrodifferential and related equations. (English) Zbl 0728.65117

The numerical solution of partial integodifferential equations (with homogeneous Dirichlet boundary conditions and given initial values) by time-continuous finite-element methods is considered. The paper presents convergence results based on the decomposition u h -u=(u h -V h u)+(V h u-u) of the error, where V h is the so-called Ritz- Volterra projection.

First, various error estimates for the Ritz-Volterra projection (in L p for 2p) are given. Separate sections are then devoted to their application to parabolic and hyperbolic integrodifferential equations, and to Sobolev and viscoelasticity type equations.

65R20Integral equations (numerical methods)
45K05Integro-partial differential equations