We consider the development of an efficient numerical method for the simulation of microwave discharge plasmas. The method uses the idea of finite element patch and can deal with very disparate length scales of the plasma. In this paper, the time-domain Maxwell's equations, which are coupled with the plasma transport equations via the time-varying electron current density, are solved with a two-level Schwarz type algorithm based on a variational formulation of the standard Yee scheme. The patch

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... of finite elements is used to calculate in an iterative manner the solution in the plasma region where a better precision is required. This numerical approach provides the Yee scheme with an efficient local-grid refinement capacity while preserving its stability. A numerical analysis shows its accuracy and computational efficiency on nested Cartesian grids. Simulation of a microwave breakdown in air under atmospheric pressure is then performed and results are discussed. We believe that both the inherent versatility with regard to the variational formulation and the efficiency of the proposed method can make it particularly suitable in modeling of microwave discharge plasmas by providing more insights of their nature and behavior.