Brunken, Julia: Stable and efficient Petrov-Galerkin methods for certain (kinetic) transport equations. 2021
Inhalt
- Introduction
- Background
- Modeling of glioma tumor spreading
- Abstract well-posedness theory
- Sobolev spaces for transport and kinetic equations
- The transport equation
- An optimally stable ultraweak (space-time) formulation
- An optimally stable Petrov-Galerkin method
- Optimally stable discrete spaces
- Nonphysical restrictions at the boundary
- Postprocessing
- Comparison with other approaches
- The reduced basis method for parametrized transport problems
- Parametrized transport problem
- Discretization
- Reduced scheme
- Basis generation
- Error analysis for the reduced basis approximation
- Comparison with the double greedy algorithm
- Computational realization
- Implementation for constant data
- Assembling the matrices for spaces on rectangular grids
- Implementation for nonconstant data
- Numerical experiments
- The kinetic Fokker-Planck equation
- Conclusion and outlook
- Discussion: Global traces in H1fp()
- Bibliography