semidiscrete finite element approximations
The stability and approximation properties of Ritz-Volterra projection and applications. II
For part I see ibid. 6, No. 1, 57-76 (1997; Zbl 0888.65117)]. The author investigates in a unified way the convergence of semidiscrete finite element approximations (Ritz-Volterra projections) to various type of evolution equations: parabolic and hyperbolic integrodifferential equations, Sobolev equation, and equations of viscoelasticity. Assuming the existence and uniqueness of sufficiently smooth solutions, the author obtains optimal order error estimates in \(L_p\) and \(W^1_p\) for \(2\leq p\leq\infty\).
scientific article; zbMATH DE number 1616507