In this work, we simulate the 2011 M9 Tohoku-Oki tsunami using new coseismic tsunami sources based on inverting onshore and offshore geodetic data, using 3D Finite Element Models (FEM). Such FEMs simulate elastic dislocations along the plate boundary interface separating the stiff subducting Pacific Plate from the relatively weak forearc and volcanic arc of the overriding Eurasian plate. Due in part to the simulated weak forearc materials, such sources produce significant shallow slip (several tens of meters) along the updip portion of the rupture near the trench. To assess the accuracy of the new approach, we compare observations and numerical simulations of the tsunami's far- and near-field coastal impact for: (i) one of the standard seismic inversion sources (UCSB; Shao et al. 2011); and (ii) the new FEM sources. Specifically, results of numerical simulations for both sources, performed using the fully nonlinear and dispersive Boussinesq wave model FUNWAVE-TVD, are compared to DART buoy, GPS tide gauge, and inundation/runup measurements. We use a series of nested model grids with varying resolution (down to 250 m nearshore) and size, and assess effects on model results of the latter and of model physics (such as when including dispersion or not). We also assess the effects of triggering the tsunami sources in the propagation model: (i) either at once as a hot start, or with the spatiotemporal sequence derived from seismic inversion; and (ii) as a specified surface elevation or as a more realistic time and space-varying bottom boundary condition (in the latter case, we compute the initial tsunami generation up to 300 s using the non-hydrostatic model NHWAVE). Although additional refinements are expected in the near future, results based on the current FEM sources better explain long wave near-field observations at DART and GPS buoys near Japan, and measured tsunami inundation, while they simulate observations at distant DART buoys as well or better than the UCSB source. None of the sources, however, are able to explain the largest runup and inundation measured between 39.5° and 40.25°N, which could be due to insufficient model resolution in this region (Sanriku/Ria) of complex bathymetry/topography, and/or to additional tsunami generation mechanisms not represented in the coseismic sources (e.g., splay faults, submarine mass failure). This will be the object of future work.