The object of this paper is a theoretical study of the convergence of approximation methods (Galerkin and finite difference methods) to compute eigenelements of a closed linear operator T in a Banach ...

It is shown that the Ritz projection onto spaces of piecewise linear finite elements is bounded in the Sobolev space, $\overset {\circ} {W}_p^1$, for $2 \leqslant p \leqslant \infty$.