Finite Element Methods for Reaction-Diffusion Systems
The figure below represents the solution of the Fitzhugh-Nagumo equations:
The solution is characterized by the formation and expansion of a scroll wave that begins forming on the boundary of R1 and spreads outward.
Solutions to such nonlinear partial differential equations are often obtained
by discretization using the finite element method.
Adaptive finite element methods seek
to improve the accuracy and efficiency
by increasing the discretization where errors are
large and decreasing it where they are small.
Thus, error estimates must be computed during the computation. These
a posteriori error estimates and the adaptive machinery that
utilizes them are the subjects of much of
Professor Moore's research.