Discontinuous Galerkin methods for the chemotaxis and haptotaxis models. (English) Zbl 1157.65449
Summary: First we formulate and compare three different discontinuous interior penalty Galerkin methods for the 2D Keller-Segel chemotaxis model. The Keller-Segel chemotaxis model is the important starting step in the modeling of a real biological system. We show in the numerical tests that two of the proposed methods fail to give accurate, oscillation-free solutions.
Next, we consider the application of the successful method for the Keller-Segel model to the simulation of the more realistic, and closely related haptotaxis model of tumor invasion into healthy tissues.
Next, we consider the application of the successful method for the Keller-Segel model to the simulation of the more realistic, and closely related haptotaxis model of tumor invasion into healthy tissues.
MSC:
| 65M60 | Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs |
| 35K57 | Reaction-diffusion equations |
| 92E20 | Classical flows, reactions, etc. in chemistry |
| 92C17 | Cell movement (chemotaxis, etc.) |
| 92-08 | Computational methods for problems pertaining to biology |
Keywords:
Keller-Segel chemotaxis model; haptotaxis model; convection-diffusion-reaction systems; discontinuous Galerkin methods; NIPG; IIPG; SIPG methods; Cartesian meshes; numerical examples; tumor invasionSoftware:
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