Numerical solution of a diffusion consumption problem with a free boundary

TLDR: In this paper, a fixed domain numerical method is presented which is motivated by a theoretical formulation developed by Rogers, and the frontal generation appears by way of a simple algebraic comparison operation involving truncation of the computed approximation.

Abstract: We consider the numerical solution of an implicit moving free boundary problem which arises in the study of diffusion and consumption of oxygen in tissue. A fixed domain numerical method is presented which is motivated by a theoretical formulation developed by Rogers. Our numerical method uses any convenient finite difference or finite element scheme which converges to the underlying partial differential equation. The frontal generation appears by way of a simple algebraic comparison operation involving truncation of the computed approximation. Higher space dimensions are treated with equal ease. Results of numerical experiments are presented. A convergence proof for the truncation method is given.