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Functionals of the meta-generalized gradient approximation (MGGA) arenowadays widely used in chemistry and solid-state physics for the simulation ofelectronic systems like molecules, solids, or surfaces. Due to their dependencyon the kinetic energy density, they are in principle more accurate than GGAfunctionals for various properties (geometry, binding energy, electronicstructure, etc.), while being nearly as fast since they are still of thesemilocal form. Thus, when an accuracy better than GGA is required, one mayconsider using a MGGA instead of the much more costly hybrid functionals ormethods like the random-phase approximation or $GW$. In this work, theself-consistent implementation of MGGA functionals in APW based methods ispresented. Technical aspects of the implementation are discussed, andcalculations of band gaps, lattice constants, and magnetic moments arepresented in order to validate our implementation. To test the changes of theelectron density due to a MGGA, the electric field gradient on transition-metalatoms is calculated.

Implementation of self-consistent MGGA functionals in augmented plane wave based methods