A remark about Galerkin method
arXiv:1705.06880
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This is a theoretical result for numerical analysts studying the limitations of Galerkin methods for linear equations.
The paper proves that for any linear equation Lu=f, the Galerkin method has at least as many unsolvable right-hand sides as there are finite-dimensional subspaces with dimension greater than five times the number of basis functions.
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 $ψ_1,..., ψ_N$ .