  The exact numerical simulation of plasma turbulence is one of the assets and
challenges in fusion research. For grid-based solvers, sufficiently fine
resolutions are often unattainable due to the curse of dimensionality. The
sparse grid combination technique provides the means to alleviate the curse of
dimensionality for kinetic simulations. However, the hierarchical
representation for the combination step with the state-of-the-art hat functions
suffers from poor conservation properties and numerical instability.
  The present work introduces two new variants of hierarchical multiscale basis
functions for use with the combination technique: the biorthogonal and full
weighting bases. The new basis functions conserve the total mass and are shown
to significantly increase accuracy for a finite-volume solution of constant
advection. Further numerical experiments based on the combination technique
applied to a semi-Lagrangian Vlasov--Poisson solver show a stabilizing effect
of the new bases on the simulations.
