European Numerical Mathematics and
Advanced Applications Conference 2019
30th sep - 4th okt 2019, Egmond aan Zee, The Netherlands
15:45   MS50: Numerical methods to advance mathematical biology research (Part 3)
Chair: Alf Gerisch
25 mins
Numerical approximations of a tractable mathematical model for tumour growth
Vanessa Styles
Abstract: We consider a free boundary problem representing one of the simplest mathematical descriptions of the growth and death of a tumour. The mathematical model takes the form of a closed interface evolving via forced mean curvature flow where the forcing depends on the solution of a PDE that holds in the domain enclosed by the interface. We derive sharp interface and diffuse interface finite element approximations of this model and present some numerical results.
25 mins
Multiscale dynamics of bulk and leading edge in cancer invasion
Dumitru Trucu
Abstract: In this talk I will present a novel multiscale moving boundary approach for cancer invasion that accounts for cell-adhesion in the context of the multiphase nature of the ECM dynamics. This connects the tissue-scale macro-dynamics with both the proteolytic cell- scale dynamics occurring at the tumour invasive edge and the micro-scale ECM fibres dynamic degradation and realignment occurring inside the tumour domain. The new modelling framework, will be accompanied by details of the computational approach and a discussion of the numerical simulation results.
25 mins
Hybrid High-Order methods in the framework of fractured porous media
Florent CHAVE, Daniele A. Di Pietro, Luca Formaggia
Abstract: In this work, we propose a model for the passive transport of a solute in a fractured porous medium, for which we develop a Hybrid High-Order (HHO) space discretization. We consider, for the sake of simplicity, the case where the flow problem is fully decoupled from the transport problem. The novel transmission conditions in our model mimic at the discrete level the property that the advection terms do not contribute to the energy balance. This choice enables us to handle the case where the concentration of the solute jumps across the fracture. The HHO discretization hinges on a mixed formulation in the bulk region and on a primal formulation inside the fracture for the flow problem, and on a primal formulation both in the bulk region and inside the fracture for the transport problem. Relevant features of the method include the treatment of nonconforming discretizations of the fracture, as well as the support of arbitrary approximation orders on fairly general meshes.