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 \(u_ h-u=(u_ h-V_ hu)+(V_ hu-u)\) 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 \(2\leq p\leq \infty)\) are given. Separate sections are then devoted to their application to parabolic and hyperbolic integrodifferential equations, and to Sobolev and viscoelasticity type equations.
First, various error estimates for the Ritz-Volterra projection (in \(L_ p\) for \(2\leq p\leq \infty)\) are given. Separate sections are then devoted to their application to parabolic and hyperbolic integrodifferential equations, and to Sobolev and viscoelasticity type equations.
Reviewer: E.Hairer (Genève)