We analyze a coupled system of evolution equations that describes the effect
of thermal gradients on the motion and deposition of N populations of
colloidal species diffusing and interacting together through Smoluchowski
production terms. This class of systems is particularly useful in studying drug
delivery, contaminant transportin complex media, as well as heat shocks
thorough permeable media. The particularity lies in the modeling of the
nonlinear and nonlocal coupling between diffusion and thermal conduction. We
investigate the semidiscrete as well as the fully discrete em a priori error
analysis of the finite elements approximation of the weak solution to a
thermo-diffusion reaction system posed in a macroscopic domain. The
mathematical techniques include energy-like estimates and compactness
arguments
