Refoundation of the Cell Method Using Augmented Dual Grids

In this paper, the cell method (CM) is reformulated using augmented dual grids. In this way, the boundary of the discretized spacial domain can be properly dealt with and energetic quantities can be introduced, overcoming the well-known drawbacks of the CM. The details are given for electromagnetic boundary value problems, whose discretization can severely suffer from such drawbacks of the CM.