Uniform convergence of operator semigroups without time regularity

Operator Semigroups for Convergence Analysis

The paper serves as a review on the basic results showing how functional analytic tools have been applied in numerical analysis. It deals with abstract Cauchy problems and present how their solutions are approximated by using space and time discretisations. To this end we introduce and apply the basic notions of operator semigroup theory. The convergence is analysed through the famous theorems ...

A General Theorem on the Convergence of Operator Semigroups

In all of these theorems the notion of convergence used in (1-1) and (1-2) has essentially been strong convergence. It is the purpose of the present paper to prove analogous theorems for a certain class of notions of convergence, which will include, in the case of Banach spaces of functions with the sup norm, bounded, pointwise convergence, and convergence of bounded sequences which is uniform ...

Convergence of nonconforming multigrid methods without full elliptic regularity

We consider nonconforming multigrid methods for symmetric positive definite second and fourth order elliptic boundary value problems which do not have full elliptic regularity. We prove that there is a bound (< 1) for the contraction number of the W -cycle algorithm which is independent of mesh level, provided that the number of smoothing steps is sufficiently large. We also show that the symme...

Strong Convergence Theorems for Nonexpansive Semigroups without Bochner Integrals

Connexion with Operator Semigroups