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Full-Text Articles in Numerical Analysis and Computation
Adaptive Discontinuous Galerkin Finite Element Methods For A Diffuse Interface Model Of Biological Growth, Andreas C Aristotelous
Adaptive Discontinuous Galerkin Finite Element Methods For A Diffuse Interface Model Of Biological Growth, Andreas C Aristotelous
Doctoral Dissertations
This PhD dissertation concentrates on the development and application of adaptive Discontinuous Galerkin Finite Element (DG-FE) methods for the numerical solution of a Cahn-Hilliard-type diffuse interface model for biological growth. Models of this type have become popular for studying cancerous tumor progression in vivo. The work in this dissertation advances the state-of-the-art in the following ways: To our knowledge the work here contains the first primitive-variable, completely discontinuous numerical implementations of a 2D scheme for the Cahn-Hilliard equation as well as a diffuse interface model of cancer growth. We provide numerical evidence that the schemes above are convergent, with the …