Ludmil Zikatanov: High order exponential fitting discretizations for convection diffusion problems

We discuss discretizations and solvers for a class of numerical methods for convection diffusion equations in arbitrary spatial dimensions. Targeted applications include the Nernst-Plank equations for transport of species in a charged media. We illustrate how such exponentially fitted methods are derived. A main step in proving error estimates is showing unisolvence for the quasi-polynomial spaces of differential forms defined as weighted spaces of differential forms with polynomial coefficients. We show that the unisolvent set of functionals for such spaces on a simplex in any spatial dimension is the same as the set of such functionals used for the polynomial spaces. We are able to prove our results without the use of Stokes' Theorem, which is the standard tool in showing the unisolvence of functionals in polynomial spaces of differential forms.
This is joint work with Shuonan Wu (Beijing University)