It is shown that the Galerkin approximation procedure is an effective representation of the solution of a computable coercive variational problem in a computable Hilbert space.
Atsushi Yoshikawa. "On computability of the Galerkin procedure." Proc. Japan Acad. Ser. A Math. Sci. 83 (5) 69 - 72, May 2007. https://doi.org/10.3792/pjaa.83.69