This paper aims to conclude a sequence of works focused on the numerical study of a system of partial differential equations in a nonuniform grid that can be used to describe the
drug release from polymeric platforms. The drug release is a consequence of the non-Fickian fluid uptake, the dissolution process and the Fickian drug transport. The development of a computational tool and its theoretical convergence support was the common driven force. In a previous work from the authors, second-order error estimates were established for the numerical approximations for the solvent, solid drug and dissolved drug considering severe smoothness assumption on the solutions: the solvent and the dissolve drug were \( C^4 \)- functions. In the present work, our aim is to establish second-order estimates for the same variables reducing the smoothness assumption, namely, we assume that the solvent and the dissolved drug are \( H^3 \)- functions. Numerical experiments illustrating the obtained theoretical results are also included.