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A semi-Lagrangian method for parabolic problems is proposed, that extendsprevious work by the authors to achieve a fully conservative, flux-formdiscretization of linear and nonlinear diffusion equations. A basic consistencyand convergence analysis are proposed. Numerical examples validate the proposedmethod and display its potential for consistent semi-Lagrangian discretizationof advection--diffusion and nonlinear parabolic problems.

Flux form Semi-Lagrangian methods for parabolic problems