  Functionals of the meta-generalized gradient approximation (MGGA) are
nowadays widely used in chemistry and solid-state physics for the simulation of
electronic systems like molecules, solids, or surfaces. Due to their dependency
on the kinetic energy density, they are in principle more accurate than GGA
functionals for various properties (geometry, binding energy, electronic
structure, etc.), while being nearly as fast since they are still of the
semilocal form. Thus, when an accuracy better than GGA is required, one may
consider using a MGGA instead of the much more costly hybrid functionals or
methods like the random-phase approximation or $GW$. In this work, the
self-consistent implementation of MGGA functionals in APW based methods is
presented. Technical aspects of the implementation are discussed, and
calculations of band gaps, lattice constants, and magnetic moments are
presented in order to validate our implementation. To test the changes of the
electron density due to a MGGA, the electric field gradient on transition-metal
atoms is calculated.
