4 papers · 1 filter
A Proximal Primal-Dual Approach to Generalized JKO Schemes for Doubly Nonlinear Parabolic Equations
Luis M. Briceño-Arias, José A. Carrillo, Dante Kalise +2
Variational methods based on optimization strategies are proposed to numerically solve a large family of nonlinear partial differential equations. They are all particular instances…
Finite Element Approximation of the Fractional Porous Medium Equation
José A. Carrillo, Stefano Fronzoni, Endre Süli
We construct a finite element method for the numerical solution of a fractional porous medium equation on a bounded open Lipschitz polytopal domain , wher…
A frame approach for equations involving the fractional Laplacian
Ioannis P. A. Papadopoulos, Timon S. Gutleb, José A. Carrillo +1
Exceptionally elegant formulae exist for the fractional Laplacian operator applied to weighted classical orthogonal polynomials. We utilize these results to construct a solver, bas…
A minimax method for the spectral fractional Laplacian and related evolution problems
José A. Carrillo, Stefano Fronzoni, Yuji Nakatsukasa +1
We present a numerical method for the approximation of the inverse of the fractional Laplacian , based on its spectral definition, using rational functions to approximat…