Spectral Approximation of Fractional PDEs in Image Processing and Phase Field Modeling - Antil, Harbir; Bartels, Sören (Journal of computational methods in applied mathematics, 2017)
Fractional differential operators provide an attractive mathematical tool to model effects with limited regularity properties. Particular examples are image processing and phase field models in which jumps across lower dimensional subsets and sharp transitions across interfaces are of interest. The numerical solution of corresponding model problems via a spectral method is analyzed. Its efficiency and features of the model problems are illustrated by numerical experiments.