A remark about Galerkin method

Abstract

In this article was proved, that any linear equation $Lu=f$ in the case of any linear versions of the Galerkin method, has at least as many unsolved right-hand sides in the form of linear combinations $f=Lψ_1 +...+Lψ_N +Lψ_{N+1} +...+Lψ_{5N} +...+Lψ_{T}$, as there are finite-dimensional linear subspaces with dimensionality as much than five times as the number of basis functions $ψ_1,..., ψ_N$ .