An Ill-designed Algorithm for Solving a Multidimensional Nonlinear Diffusion Equation in a Domain Limited By a Moving Boundary

Deleersnijder, Eric
(1994) Mathematical and Computer Modelling — Vol. 19, n° 10, p. 75-81 (1994)

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Abstract
In the Appendix of [1], a numerical method was suggested for solving two-dimensional, nonlinear, advection-diffusion equations in a domain limited by a moving boundary. A theoretical analysis reveals that, in most cases, the velocity of the boundary must be predicted to be zero. This undesirable behaviour stems from the incompatibility of the nonlinear numerical stability condition and the criterion allowing the boundary to move. An improvement to the algorithm is briefly outlined.
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Deleersnijder, E. (1994). An Ill-designed Algorithm for Solving a Multidimensional Nonlinear Diffusion Equation in a Domain Limited By a Moving Boundary. Mathematical and Computer Modelling, 19(10), 75-81. https://doi.org/10.1016/0895-7177(94)90107-4 (Original work published 1994)