We present a self-consistent, continuum model for the growth of a vicinal facet from solution, which couples surface phenomena and bulk effects. The surface kinetic model, based on the theory of Burton, Cabrera, and Frank (BCF), rigorously accounts for the interactions of discrete growth steps through surface diffusion fields, adsorption and desorption events, ledge growth kinetics with Schwoebel effects, and convective transport due to step motion. This model is self-consistently coupled with a bulk transport model which describes bulk diffusion to terraces, direct bulk diffusion to growth steps, and bulk convective transport due to step motion and applied flow fields. No analytical approximations are made, rather the simultaneous governing equations are solved numerically by an efficient, moving boundary finite element method. Results from a number of benchmark simulations are discussed.