A Stabilized Finite Element Method for Morpho-Visco-Poroelastic Model

Abstract: We propose a mathematical model that combines elastic, viscous and porous effects with growth or shrinkage due to microstructural changes. This phenomenon is important in tissue or tumor growth, as well as in dermal contraction. Although existence results of the solution to the problem are not given, the current study assesses stability of the equilibria for both the continuous and semi-discrete versions of the model. Furthermore, a numerical condition for monotonicity of the numerical solution is described, as well as a way to stabilize the numerical solution so that spurious oscillations are avoided. The derived stabilization result is confirmed by computer simulations. In order to have a more quantitative picture, the total variation has been evaluated as a function of the stabilization parameter.