14:30
14:30
15:30
Zonal flows in Giant Planets : anelastic rotating convection models
14:00
Scale-inariant moving finite elements for time-dependent nonlinear partial differential equations
Abstract
A scale-invariant moving finite element method is proposed for the
adaptive solution of nonlinear partial differential equations. The mesh
movement is based on a finite element discretisation of a scale-invariant
conservation principle incorporating a monitor function, while the time
discretisation of the resulting system of ordinary differential equations
may be carried out using a scale-invariant time-stepping. The accuracy and
reliability of the algorithm is tested against exact self-similar
solutions, where available, and a state-of-the-art $h$-refinement scheme
for a range of second and fourth order problems with moving boundaries.
The monitor functions used are the dependent variable and a monitor
related to the surface area of the solution manifold.