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The recursive convolution method to treat linear dispersive materials in the finite difference time domain (FDTD) is here generalized to an explicit finite volume solver and an implicit finite element solver. Both solvers are interfaced to FDTD resulting in two hybrid solvers. The stability of the solvers is analyzed and the accuracy is demonstrated in several scattering cases, where a plane wave illuminates a sphere with complex permittivity. Excellent agreement with the analytical Mie series solution is obtained for materials of Debye and Lorentz type as well as for a material consisting of two Lorentz poles.