Disputas: Franziska Weber
M.Sci Franziska Weber ved Matematisk institutt vil forsvare sin avhandling for graden ph.d.:
Convergent Numerical Methods for Nonlinear Partial Differential Equations
Tid og sted for prøveforelesning
Professor Andreas Prohl, Universität Tübingen
Professor Anders Szepessy, Kungliga Tekniska högskolan
Professor Giulia Di Nunno, Universitetet i Oslo
Leder av disputas
Professor Hans Brodersen, Matematisk institutt, Universitet i Oslo
- Professor Nils Henrik Risebro, Matematisk institutt, Universitet i Oslo
- Professor Helge Holden, Institutt for matematiske fag, Norges teknisk-naturvitenskapelige universitet
Partial differential equations (PDEs) are a powerful tool to describe a variety of phenomena in engineering, physics, astronomy, biology and economics in a mathematical way. However, as the models are typically quite complex, solutions to the PDEs cannot be computed by hand, and numerical algorithms are needed to compute approximations to the solutions using computers. In this thesis, such numerical methods for PDEs with applications in reservoir simulation, complex fluids and modeling of tumor growth are designed, analyzed and tested in computer simulations.
The equations considered are of nonlinear hyperbolic type. The nonlinearities give rise to complicated behavior of the solutions: Shock waves, oscillations and blow-ups may occur. This renders analysis and approximation of solutions to nonlinear equations challenging. In order to construct accurate methods for the approximation of such models, the underlying nonlinear structure of the equations has to be taken into account and reproduced at the level of the approximations.
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