In this talk, we present a numerical analysis of the Eyles-King-Styles tumor growth model, a free boundary problem coupling a Poisson equation in the bulk \Omega with forced mean curvature flow on the surface \Gamma. Unlike existing evolving bulk problems or evolving surface problems, this bulk-surface coupling necessitates H^{1/2}-order analysis on the surface \Gamma. We establish a comprehensive H^{1/2}(\Gamma) framework that captures the coupling between the bulk and surface. This framework enables our discretization to admit a rigorous convergence analysis for continuous finite elements of polynomial degree at least three, yielding optimal-order H^1(\Omega)/H^{1/2}(\Gamma) error bounds.