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A large class of scalar-tensor theories of gravity exhibit a screeningmechanism that dynamically suppresses fifth forces in the Solar system andlocal laboratory experiments. Technically, at the scalar field equation level,this usually translates into nonlinearities which strongly limit the scope ofanalytical approaches. This article presents $femtoscope$ $-$ a Pythonnumerical tool based on the Finite Element Method (FEM) and Newton method forsolving Klein-Gordon-like equations that arise in particular in the symmetronor chameleon models. Regarding the latter, the scalar field behavior isgenerally only known infinitely far away from the its sources. We thusinvestigate existing and new FEM-based techniques for dealing with asymptoticboundary conditions on finite-memory computers, whose convergence are assessed.Finally, $femtoscope$ is showcased with a study of the chameleon fifth force inEarth orbit.

Solving nonlinear Klein-Gordon equations on unbounded domains via the Finite Element Method