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Mathematical Modelling of Tumour Dormancy

K. M. Page — 2009

Mathematical Modelling of Natural Phenomena

Many tumours undergo periods in which they apparently do not grow but remain at a roughly constant size for extended periods. This is termed tumour dormancy. The mechanisms responsible for dormancy include failure to develop an internal blood supply, individual tumour cells exiting the cell cycle and a balance between the tumour and the immune response to it. Tumour dormancy is of considerable importance in the natural history of cancer. In many cancers, and in particular in breast cancer, recurrence...

Each H1/2–stable projection yields convergence and quasi–optimality of adaptive FEM with inhomogeneous Dirichlet data in Rd

M. Aurada;  M. Feischl;  J. Kemetmüller;  M. Page;  D. Praetorius — 2013

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

We consider the solution of second order elliptic PDEs in R with inhomogeneous Dirichlet data by means of an –adaptive FEM with fixed polynomial order  ∈ N. As model example serves the Poisson equation with mixed Dirichlet–Neumann boundary conditions, where the inhomogeneous Dirichlet data are discretized by use of an –stable projection, for instance, the –projection for  = 1 or the Scott–Zhang projection for general  ≥ 1. For error estimation, we use a residual error...

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